Abstract. We consider the five-component Meinhardt-Gierer model for mutually exclusive patterns and segmentation which was proposed in [11]. We prove rigorous results on the existence and stability...
MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R 2 (2009)
Manuel Del Pino, Frank Pacard, Juncheng Wei
Abstract. We construct new class of entire solutions of the Allen-Cahn equation ∆u+(1−u 2)u = 0, in R 2 ( ∼ C). Given k ≥ 1, we find a family of solutions whose zero level sets are, away from...
ON DE GIORGI CONJECTURE IN DIMENSION N ≥ 9 (2009)
Manuel Del Pino, Michal Kowalczyk, Juncheng Wei
Abstract. A celebrated conjecture due to De Giorgi states that any bounded solution of the equation ∆u+(1−u2)u = 0 in RN with ∂yN u> 0 must be such that its level sets {u = λ} are all...
Manuel Del Pino, Michal Kowalczyk, Juncheng Wei
Abstract. — We consider minimal surfaces M which are complete, embedded and have finite total curvature in R3, and bounded, entire solutions with finite Morse index of the Allen-Cahn equation...
Abstract. We consider the following Gierer-Meinhardt system in R1: At = ɛ (2009)
In R, Juncheng Wei, Matthias Winter, A Ap, H Ar
(−1) = H ′ (1) = 0, where (p, q, r, s) satisfy qr 1 < < +∞, 1 < p < +∞,
A COUNTEREXAMPLE TO A CONJECTURE BY DE GIORGI IN LARGE DIMENSIONS (2009)
Abstract. We consider the Allen-Cahn equation ∆u + u(1 − u 2) = 0 in R N. A celebrated conjecture by E. De Giorgi (1978) states that if u is a bounded solution to this problem such that ∂xN...
STABILITY OF CURVED INTERFACES IN THE PERTURBED TWO-DIMENSIONAL ALLEN–CAHN SYSTEM ∗ (2009)
David Iron, Theodore Kolokolonikov, John Rumsey, Juncheng Wei
Abstract. We consider { the singular limit of a perturbed Allen–Cahn model on a bounded two-ut = ε2Δu − 2(u − εa)(u2 − 1), x ∈ Ω ⊂ R2 dimensional domain: where ε is a small parameter...
Theodore Kolokolnikov, Juncheng Wei, Matthias Winter
Abstract. We study the Gierer-Meinhardt system in one dimension in the limit of large reaction rates of the activator. Three solution types are considered: (i) an interior spike; (ii) a boundary...
SPIKES FOR THE GIERER-MEINHARDT SYSTEM WITH DISCONTINUOUS DIFFUSION COEFFICIENTS (2009)
Abstract. We rigorously prove results on spiky patterns for the Gierer-Meinhardt system [10] with a jump discontinuity in the diffusion coefficient of the inhibitor. Using numerical computations in...
Philip K. Maini, Juncheng Wei, Matthias Winter, Ω Rn
ξq, x ∈ Ω, t>0, τ|Ω|ξt = −|Ω|ξ + 1 ξs ∫ Ω Ar dx, t> 0 with Robin boundary condition ɛ ∂A ∂ν + aAA =0, x ∈ ∂Ω, where aA> 0, the positive reaction rates (p, q,...
SPIKES FOR THE GIERER-MEINHARDT SYSTEM WITH MANY SEGMENTS OF DIFFERENT DIFFUSIVITIES (2009)
Wang Hung Tse, Juncheng Wei, Matthias Winter
Abstract. We rigorously prove results on spiky patterns for the Gierer-Meinhardt system [5] with a large number of jump discontinuities in the diffusion coefficient of the inhibitor. Using numerical...
Homoclinic solutions for fourth order traveling wave equations (2009)
Santra, Sanjiban, Wei, Juncheng
We consider homoclinic solutions of fourth order equations $$ u^{""} + \beta^2 u^{"} + V_u (u)=0 {in} \R ,$$ where $V(u)$ is either the suspension bridge type $V(u)=e^u-1-u$ or Swift-Hohenberg type $...
Non-compactness of the Prescribed Q-curvature Problem in Large Dimensions (2009)
Let $(M, g)$ be a compact Riemannian manifold of dimension $N \geq 5$ and $Q_g$ be its $Q$ curvature. The prescribed $Q$ curvature problem is concerned with finding metric of constant $Q$ curvature...
Del Pino, Manuel, Kowalczyk, Mike, Wei, Juncheng
We consider minimal surfaces $M$ which are complete, embedded and have finite total curvature in $\R^3$, and bounded, entire solutions with finite Morse index of the Allen-Cahn equation $\Delta u +...
N+2p On Conformally Invariant Equation (-A)P u- K(x) u N-2, = 0 and Its Generalizations (*). (2008)
Guozhen Lu, Juncheng Wei, Xingwang Xu
Abstract.- We consider the question of existence and non-existence of positive entire solutions for con-formally invariant equations involving polyharmonic operator. We obtain existence of infinitely...
On De Giorgi Conjecture in Dimension $N \geq 9$ (2008)
Del Pino, Manuel, Kowalczyk, Mike, Wei, Juncheng
A celebrated conjecture due to De Giorgi states that any bounded solution of the equation $\Delta u + (1-u^2) u = 0 \hbox{in} \R^N $ with $\pp_{y_N}u >0$ must be such that its level sets $\{u=\la\}$...
Transition layer for the heterogeneous Allen–Cahn equation (2008)
Mahmoudi, Fethi, Malchiodi, Andrea, Wei, Juncheng
We consider the equation $\e^{2}\Delta u=(u-a(x))(u^2-1)$ in $\Omega$, $\frac{\partial u}{\partial \nu} =0$ on $\partial \Omega$, where $\Omega$ is a smooth and bounded domain in $\R^n$, $\nu$ the...
Infinitely many solution for prescribed curvature problem on $S^N$ (2008)
We consider the following prescribed scalar curvature problem on $ S^N$ (*)$$\left\{\begin{array}{l} - \Delta_{S^N} u + \frac{N(N-2)}{2} u = \tilde{K} u^{\frac{N+2}{N-2}} {on} S^N, u >0...
Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^N$ (2008)
We consider the following nonlinear problem in $\R^N$ $$\label{eq} - \Delta u +V(|y|)u=u^{p},\quad u>0 {in} \R^N, u \in H^1(\R^N) $$ where $V(r)$ is a positive function, $11$, $\theta>0$, and...
EXISTENCE AND STABILITY OF SPHERICALLY LAYERED SOLUTIONS OF THE DIBLOCK COPOLYMER EQUATION ∗ (2008)
Abstract. The relatively simple Ohta–Kawasaki density functional theory for diblock copolymer melts allows us to construct and analyze exact solutions to the Euler–Lagrange equation by singular...
NONRADIAL CLUSTERED SPIKE SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS ON S n (2008)
Catherine Bandle, Juncheng Wei
Abstract. We consider the following superlinear elliptic equation on S n ε 2 ∆S nu − u + up = 0 in S n, u> 0 in S n where ∆S n is the Laplace-Beltrami operator on Sn. We prove that for any...
Conventionally, to learn wave collapse and optical turbulence, one must study finite-time blow-up solutions of one-component self-focusing nonlinear Schrödinger equations (NLSE). Here we consider...
SYMBIOTIC BRIGHT SOLITARY WAVE SOLUTIONS OF COUPLED NONLINEAR SCHRÖDINGER EQUATIONS (2008)
Abstract. Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when selfinteraction becomes...
Radial solutions and phase separation in a system of two coupled Schrödinger equations (2008)
−∆u + u − u 3 − βv 2 u = 0 in B, −∆v + v − v 3 − βu 2 v = 0 u, v> 0 in B, u = v = 0 in B, on ∂B, where N ≤ 3 and B ⊂ R N is the unit ball. We show that, for every β ≤...
Boundary interface for the Allen-Cahn equation, preprint (2008)
Abstract. We consider the Allen-Cahn equation ε 2 ∆u + u − u 3 = 0 in Ω, ∂u = 0 on ∂Ω, ∂ν where Ω is a smooth and bounded domain in Rn such that the mean curvature is positive at...
Thomas Bartsch, Zhi-qiang Wang, Juncheng Wei, Edward Fadell
Abstract. We consider the existence of bound states for the coupled elliptic system ∆u1 − λ1u1 + µ1u 3 1 + βu 2 2u1 = 0 in R n, ∆u2 − λ2u2 + µ2u 3 2 + βu 2 1u2 = 0 in R n, u1> 0,...
Transition Layer for the Heterogeneous Allen-Cahn Equation (2008)
Fethi Mahmoudi, Andrea Malchiodi, Juncheng Wei
abstract. We consider the equation (1) ε 2 ∆u = (u − a(x))(u 2 − 1) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in Rn, ν the outer unit normal to ∂Ω, and a...
Elliptique Couplé, Juncheng Wei
Abstract. We study the following system of Schrödinger-Maxwell equations ε 2 ∆v − v − ωvφ + f(v) = 0, ∆φ + γv 2 = 0 in Ω, v, φ> 0 in Ω, v, φ = 0 on ∂Ω, where Ω is a...
Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler (2008)
Juncheng Wei, Dong Ye, Feng Zhou, Département De Mathématiques
equation
MULTIPLE CLUSTERED LAYER SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS ON S n (2008)
Catherine Bandle, Juncheng Wei
Abstract. We consider the following superlinear elliptic equation on Sn j ε2∆Snu − u + f(u) = 0 in D; u> 0 in D and u = 0 on ∂D, where D is a geodesic ball on Sn with geodesic radius θ1,...
Xiaoyan Shi, Ling Xi, Danhui Weng, Xiaohong Song, Peng Wu, Beibei Wang, ...
To investigate the roles of VEGF-C, VEGFR-3 and cyclooxygenase-2 (COX-2) in tumor progression and lymph node metastasis. The expression of VEGF-C, VEGFR-3 and COX-2 were examined in 93 cases of...
Infinitely many turning points for an elliptic problem with a singular non-linearity (2008)
We consider the problem − Δ u = λ |x|α/(1 − u)p in B, u = 0 on ∂ B, 0 < u < 1 in B, where α ≥ 0, p ≥ 1 and B is the unit ball in ℝN (N ≥ 2). We show that there exists a λ* > 0...
Oval shaped droplet solutions in the saturation process of some (2008)
pattern formation problems
this paper we denote such least energy solutions by u p . Our goal here is to understand the asymptotic behavior of u p as p, serving as a parameter, approaches 1. It is known in [10] that for the...
On a Semilinear Elliptic Equation in R² when the Exponent Approaches Infinity (2007)
Xiaofeng Ren, Juncheng Wei, The L
We consider a semilinear elliptic equation in R 2 with the nonlinear exponent approaching infinity. In contrast to the blow-up behavior of the corresponding problem in R n with n 3, the L 1 (R 2 )...
Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei
In a singularly perturbed limit of small diusivity " of one of the two chemical species, equilibrium spike solutions to the Gray-Scott model on a bounded one-dimensional domain in the low...
Abstract. We consider the following singularly perturbed semilinear elliptic problem: (I)
ON THE GIERER-MEINHARDT SYSTEM WITH SATURATION (2007)
Abstract. We consider the following shadow system of the Gierer-Meinhardt system with saturation: 8
Molecular Chirality and Soliton-Stripe Pattern in Liquid Crystal Films y (2007)
The chiral liquid crystal film is a system of two coupled fields: A scalar field which represents the chirality of the molecules and a vector field which represents the direction of the molecules. In...
UNIQUENESS OF MULTIPLE-SPIKE SOLUTIONS VIA THE METHOD OF MOVING PLANES (2007)
Abstract. We study the uniqueness of multiple-spike solutions for some singularly perturbed Neumann problem in a ball. We are able to completely classify all two-peaked solutions. We can also...
Henri Berestycki, Juncheng Wei
Abstract. We consider the following singularly perturbed elliptic problem ffl
Abstract. We consider the following semilinear elliptic equation with singular nonlinearity: \Deltau \Gamma
well-known Moser-Trudinger inequality ensures the nonlinear functional J ae (u) is bounded from below if and only if ae ae 2n: = 2
John Norbury, Juncheng Wei, Matthias Winter
B t = oeB xx + (A 2) xx; x 2 R; t? 0; A(x; t) has period L where? oe? 0. For any finite L, we completely classify the existence of solutions with minimal period and the stability and instability of...
Abstract. We consider the following shadow system of Gierer-Meinhardt model 8
John Norbury, Juncheng Wei, Matthias Winter
B t = oeB xx + (A 2) xx; x 2 R; t? 0; A(x; t) has period L where? oe? 0. For any finite L, we completely classify the existence of solutions with minimal period L and determine the stability and...
ON INTERACTING BUMPS OF SEMI-CLASSICAL STATES OF NONLINEAR SCHR ODINGER EQUATIONS (2007)
Abstract. We study concentrated positive bound states of the following nonlinear Schrodinger equation h
MULTI-INTERIOR-SPIKE SOLUTIONS FOR THE CAHN-HILLIARD EQUATION WITH ARBITRARILY MANY PEAKS (2007)
Abstract. We study the Cahn-Hilliard equation in a bounded domain without any symmetry assumptions. We prove that for any fixed positive integer K there exist interior K--peak solutions whose peaks...
Existence and stability of singular patterns in the presence of a symmetry group, submitted (2007)
John Norbury, Juncheng Wei, Matthias Winter
Abstract. We study singular patterns in a particular system of parabolic partial differential equations in the presence of a group symmetry. We prove existence of the three simplest concentrated...
Abstract. We discuss the existence, uniqueness and multiplicity of large solutions of the equation \Deltau + u
; ( is an unknown constant) (2007)
Abstract. We consider the following nonlinear elliptic equations \Deltau + u N
Guozhen Lu, Juncheng Wei, N Oe D, Gamma S
Abstract. In this note we consider the following Sobolev inequality jj4OEjj 2 S 2 jjOEjj 2N
UNIQUENESS AND A PRIORI ESTIMATES FOR SOME NONLINEAR ELLIPTIC NEUMANN EQUATIONS IN R (2007)
Abstract. Under some conditions on f(u), we show that for small, the only solutions to the following elliptic equation ae \Deltau \Gamma u + f(u) = 0 in\Omega u? 0 in\Omega
Manuel Del Pino, Juncheng Wei, H In Ir
Abstract. We consider the stationary Gierer-Meinhardt system
Abstract. We study a large reaction-diffusion system which arises in the modeling of catalytic networks and describes the emerging of cluster states. We construct single cluster solutions on the real...
Abstract. We study concentrated bound states of the SchrodingerNewton equations 8
Abstract. We show that for ff 1 2, the following inequality holds: ff 2
THE STUDY OF A NONLOCAL EIGENVALUE PROBLEM (2007)
Abstract. We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for the Sel'kov model, the Gray-Scott system and angiogenesis. We give some...
Spikes for the two-dimensional Gierer-Meinhardt system: the weak coupling case (2007)
Abstract. In this paper, we rigorously prove the existence and stability of multiple-peaked patterns for the singularly perturbed GiererMeinhardt system in a two dimensional domain which are far from...
On a hypercycle system with nonlinear rate. To appear: Methods (2007)
Abstract. We study a (N + 1)\Gammahypercyclical reaction-diffusion system with nonlinear rate p. It is shown that there exists a critical threshold N 0 such that for N N 0 the system is stable while...
Gierer-meinhardt System, The Strong, Juncheng Wei, Matthias Winter
Abstract. Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also...
Abstract. We study the properties of single boundary spike solutions for the following singularly perturbed problem ffl 2
Abstract. We consider the problem ae
Higher Order Energy Expansions For Some Singularly Perturbed Neumann Problems (2007)
We consider the following singularly perturbed semilinear elliptic problem: in\Omega where\Omega is a bounded smooth domain in R , ffl ? 0 is a small constant and p is a subcritical exponent. Let J...
Juncheng Wei And, Juncheng Wei, Matthias Winter
We consider the following shadow system of the Gierer-Meinhardt model: ! A xx \Gamma A+ 0 A A ? 0; A x (0; t) = A x (1; t) = 0; where 1 ! p ! +1; 2q ? s + 1; s 0, and ? 0. It is known that a...
Asymmetric Spotty Patterns, Juncheng Wei, Matthias Winter
In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers...
On bound states concentrating on spheres for the Maxwell-Schrödinger equation (2007)
Abstract. We study the semiclassical limit for the following system of Maxwell-Schrodinger equations: \Gamma
The Toda system and multiple-end solutions of autonomous planar elliptic problems (2007)
Del Pino, Manuel, Kowalczyk, Michał, Pacard, Frank, Wei, Juncheng
We construct a new class of positive solutions for a classical semilinear elliptic problem in the plane which arise for instance as the standing-wave problem for the standard nonlinear Schr\"odinger...
Properties of positive solutions of an Elliptic Equation with negative exponents (2007)
In this paper, we study the existence and non-existence result of positive solutions to a singular elliptic equation with negative power on the bounded smooth domain or in the whole Euclidean space....
Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition (2007)
Robert, Frederic, Wei, Juncheng
We consider asymptotic behavior of the following fourth order equation \[ \Delta^2 u= \rho \frac{e^{u}}{\int_\Om e^{u} dx} {in} \Om, u= \partial_\nu u=0 {on} \partial \Omega \] where $\Om$ is a...
Half-Skyrmions and Spike-Vortex Solutions of Two-Component Nonlinear Schrodinger Systems (2007)
Recently, skyrmions with integer topological charges have been observed numerically but have not yet been shown rigorously on two-component systems of nonlinear Schrodinger equations (NLSE)...
Transition Layer for the Heterogeneous Allen-Cahn Equation (2007)
Mahmoudi, Fethi, Malchiodi, Andrea, Wei, Juncheng
We consider the equation $\e^{2}\Delta u=(u-a(x))(u^2-1)$ in $\Omega$, $\frac{\partial u}{\partial \nu} =0$ on $\partial \Omega$, where $\Omega$ is a smooth and bounded domain in $\R^n$, $\nu$ the...
Standing waves for supercritical nonlinear Schrodinger equations (2007)
Dávila, Juan, Pino, Manuel Del, Musso, Mónica, Wei, Juncheng
Publicación ISI
Supercritical elliptic problems in domains with small holes (2007)
Del Pino, Manuel, Wei, Juncheng
Publicación ISI
Standing waves for supercritical nonlinear Schrodinger equations (2007)
Davila, Juan, Del Pino, Manuel, Musso, Monica, Wei, Juncheng
Publicación ISI
Supercritical elliptic problems in domains with small holes (2007)
Pino, Manuel Del, Wei, Juncheng
Publicación ISI
Stationary Multiple Spots for Reaction-Diffusion Systems (2007)
Abstract. In this paper, we review analytical methods for a rigorous study of the existence and stability of stationary, multiple spots for reaction-diffusion systems. We will consider two classes of...
E. N. Dancer, Juncheng Wei, Tobias Weth
Abstract. We study the set of solutions of the nonlinear elliptic system
Symbiotic Bright Solitary Wave Solutions of Coupled Nonlinear Schrodinger Equations (2006)
Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrodinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it...
Singular limits of a two-dimensional boundary value problem arising in corrosion modelling (2006)
Dávila, Juan, Pino, Manuel Del, Musso, Mónica, Wei, Juncheng
We consider the boundary value problem Du = 0 in Omega, partial derivative u/partial derivative v = 2 lambda sinh u on partial derivative Omega where Omega is a smooth and bounded domain in R-2 and...
Collapsing steady states of the Keller-Segel system (2006)
Pino, Manuel Del, Wei, Juncheng
We consider the boundary value problem: Delta u - au + epsilon(2)e(u) = 0, u > 0 in Omega, sigma u/sigma v = 0 on sigma Omega, which is equivalent to the stationary Keller-Segel system from...
Half-Skyrmions and Spike-Vortex Solutions of Two-Component Nonlinear Schrödinger Systems (2006)
Recently, skyrmions with integer topological charges have been observed numerically but have not yet been shown rigorously on two-component systems of nonlinear Schrödinger equations (NLSE)...
Bubbling Solutions for an Anisotropic Emden-Fowler Equation (2006)
Juncheng Wei, Dong Ye, Feng Zhou
Abstract We consider the anisotropic Emden-Fowler equation: ∇(a(x)∇u) + ε 2 a(x)e u = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R 2 is a smooth bounded domain and a(x) is a positive, smooth...
Resonance and interior layers in an inhomogeneous phase transition model (2006)
Pino, Manuel Del, Kowalczyk, Michal, Wei, Juncheng
We consider the problem epsilon(2)Delta u + (u - a(x))(1 - u(2)) = 0 in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega is a smooth and bounded domain in...
Mesa-type patterns in the one-dimensional Brusselator and their stability (2005)
Kolokolnikov, Theodore, Erneux, Thomas, Wei, Juncheng
The Brusselator is a generic reaction-diffusion model for a tri-molecular chemical reaction. We consider the case when the input and output reactions are slow. In this limit, we show the existence of...
Wriggled lamellar solutions and their stability in the diblock copolymer problem. preprint (2005)
In a diblock copolymer system the free energy field depends nonlocally on the monomer density field. In addition there are two positive parameters in the constitutive relation. One of them is small...
Ground state of N coupled nonlinear Schrödinger equations (2005)
Abstract. We establish some general theorems for the existence and nonexistence of ground state solutions of a steady-state N coupled nonlinear Schrodinger equations. The sign of coupling constants...
Concentrating solutions for the Hénon equation 2 ∗ in IR (2005)
Pierpaolo Esposito, Angela Pistoia, Juncheng Wei
We consider the boundary value problem ∆u + |x | 2α u p = 0, α> 0, in the unit ball B with homogeneous Dirichlet boundary condition and p a large exponent. We find a condition which ensures...
On a Cubic-Quintic Ginzburg-Landau Equation with Global Coupling (2004)
Juncheng Wei, Matthias Winter, Gamma A
Abstract. We study standing wave solutions in a parabolic partial differential equations which consists of a cubic-quintic equation stabilized by global coupling A t = \DeltaA + A + cA 3
Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei
The existence, stability, and pulse-splitting behavior of spike patterns in the one-dimensional Gray-Scott model on a finite domain is analyzed in the semi-strong spike-interaction regime. This...
Numerical Challenges for Resolving Spike Dynamics for Two Reaction-Diffusion Systems (2003)
Wentao Sun, Tao Tang, Michael J. Ward, Juncheng Wei
Asymptotic and numerical methods are used to highlight dierent types of dynamical behaviors that occur for the motion of a localized spike-type solution to the singularly perturbed Gierer-Meinhardt...
Existence and stability of multiple spot solutions for the Gray-Scott model (2003)
Abstract. In this paper, we rigorously prove the existence and stability of multiple spot patterns for the Gray-Scott system in a two dimensional domain which are far from spatial homogeneity. The...
Triblock copolymer theory: Ordered ABC lamellar phase (2003)
The ABC lamellar phase of a triblock copolymer in the strong segregation region is studied with the periodic and Neumann boundary conditions. In the periodic case we prove the existence of local...
On the Spectra of 3-D Lamellar Solutions of the Diblock Copolymer Problem (2003)
One-dimensional free energy local minimizers are viewed as three-dimensional lamellar type critical points in a box. To determine whether they model the lamellar phase of diblock copolymers in the...
Nucleation in the FitzHugh-Nagumo System: Interface-Spike Solutions (2003)
We find nucleation solutions of N interfaces and K spikes to the one-dimensional FitzhHughNagumo system. Each spike sits asymptotically in the middle between two interfaces. We use the...
Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei
z Abstract Results for the existence, stability, and pulse-splitting behavior of spike patterns in the onedimensional Gray-Scott model on a finite domain in the semi-strong spike-interaction regime...
Norbury, John, Wei, Juncheng, Winter, Matthias
We study singular patterns in a particular system of parabolic partial differential equations which consist of a Ginzburg–Landau equation and a mean field equation. We prove the existence of the...
The Existence and Stability of Asymmetric Spike Patterns for the Schnakenburg Model (2002)
Asymmetric spike patterns are constructed for the two-component Schnakenburg reactiondi #usion system in the singularly perturbed limit of a small di#usivity of one of the components. For a pattern...
Wentao Sun, Tao Tang, Michael J. Ward, Juncheng Wei
Asymptotic and numerical methods are used to highlight different types of dynamical behaviors that occur for the motion of a localized spike-type solution to the singularly perturbed Gierer-Meinhardt...
The Existence and Stability of Asymmetric Spike Patterns for the Schnakenburg Model (2002)
Abstract Asymmetric spike patterns are constructed for the two-component Schnakenburg reaction-diffusion system in the singularly perturbed limit of a small diffusivity of one of the components. For...
Norbury, John, Wei, Juncheng, Winter, Matthias
We study singular patterns in a particular system of parabolic partial differential equations which consist of a Ginzburg–Landau equation and a mean field equation. We prove the existence of the...
On two dimensional Gray-Scott model: existence of single pulse solutions and their stability (2001)
Abstract. Gray-Scott model has been studied extensively in recent years. However, most of the results are in one dimensional. In this paper, we study the 2-D Gray-Scott system. We first construct two...
The Stability of Spike Solutions to the One-Dimensional Gierer-Meinhardt Model (2001)
David Iron, Michael J. Ward, Juncheng Wei
The stability properties of an N-spike equilibrium solution to the Gierer-Meinhardt activator-inhibitor model in a one-dimensional domain is studied asymptotically in the limit of small activator...
On the multiplicity of solutions of two nonlocal variational problems (2000)
We study two nonlocal variational problems in this paper. One models micro-phase separation of diblock copolymers and the other models solid-solid phase transformations that lead to fine structures....
Equilibrium solutions to the one-dimensional Gierer-Meinhardt model in the form of sequences of spikes of dierent heights are constructed asymptotically in the limit of small activator diusivity...
The Stability of Spike Solutions to the One-Dimensional Gierer-Meinhardt Model (2000)
David Iron, Michael J. Ward, Juncheng Wei, Where D
The stability properties of an N-spike equilibrium solution to a simpli ed form of the GiererMeinhardt activator-inhibitor model in a one-dimensional domain is studied asymptotically in the limit of...
Abstract. We study the interior spike solutions to a steady state problem of the shadow system of the Gierer-Meinhardt system arising from biological pattern formation. We first show that at a...
Abstract. We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in the Gierer-Meinhardt system and generalized Gray-Scott system. We give...
On a nonlocal eigenvalue problem (1998)
Abstract. We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in some reaction-diffusion systems. We give some sufficient (and explicit)...
Guozhen Lu, Juncheng Wei, Communicated Thomas Wolff
Abstract. Let G be a nilpotent, stratified homogeneous group, and let X1,...,Xm be left invariant vector fields generating the Lie algebra G associated to G. The main goal of this paper is to study...
Counting Peaks of Solutions to Some Quasilinear Elliptic Equations with Large Exponents (1995)
We consider the asymptotic behavior of certain solutions to a quasilinear problem with large exponent in the nonlinearity. Starting with the investigation of a Sobolev embedding, we get a sharp...
Qualitative properties of some semilinear elliptic equations / (1994)
Thesis (Ph. D.)--University of Minnesota, 1994.
On A Two Dimensional Elliptic Problem With Large Exponent In Nonlinearity (1994)
. A semilinear elliptic equation on a bounded domain in R 2 with large exponent in the nonlinear term is studied in this paper. We investigate positive solutions obtained by the variational method....
Spikes for the Gierer-Meinhardt System in Two Dimensions: The Strong Coupling Case (0000)
Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently...
Spikes for the Gierer-Meinhardt System in Two Dimensions: The Strong Coupling Case
Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently...
Biliverdin Reductase Mediates Hypoxia-Induced EMT via PI3-Kinase and Akt
Zeng, Rui, Yao, Ying, Han, Min, Zhao, Xiaoqin, Liu, Xiao-Cheng, Wei, Juncheng, ...
Chronic hypoxia in the renal parenchyma is thought to induce epithelial-to-mesenchymal transition (EMT), leading to fibrogenesis and ultimately end-stage renal failure. Biliverdin reductase, recently...
David Iron, Juncheng Wei, Matthias Winter
Abstract. We consider the following Schnakenberg model on the interval
Juncheng Wei, Matthias Winter, Gamma A, Gamma H +a
Abstract. We consider the following static Gierer-Meinhardt system in a bounded interval: 8
Juncheng Wei, Matthias Winter, Gamma H
Abstract. We consider the following Gierer-Meinhardt system in R 1
In the limit of small activator diffusivity ε, the stability of symmetric k-spike equilibrium solutions to the Gierer-Meinhardt reaction-diffusion system in a one-dimensional spatial...