Fractal porous media equation (2010)
Biler, Piotr, Imbert, Cyril, Karch, Grzegorz
We study a generalization of the porous medium equation involving nonlocal terms. In particular, the $L^p$ decay of solutions of the Cauchy problem is proved. Explicit self-similar solutions with...
Fractal porous media equation (2010)
Biler, Piotr, Imbert, Cyril, Karch, Grzegorz
We study a generalization of the porous medium equation involving nonlocal terms. In particular, the $L^p$ decay of solutions of the Cauchy problem is proved. Explicit self-similar solutions with...
Fractal porous media equation (2010)
Biler, Piotr, Imbert, Cyril, Karch, Grzegorz
We study a generalization of the porous medium equation involving nonlocal terms. In particular, the $L^p$ decay of solutions of the Cauchy problem is proved. Explicit self-similar solutions with...
Biler, Piotr, Corrias, Lucilla, Dolbeault, Jean
In two space dimensions, the parabolic-parabolic Keller--Segel system shares many properties with the parabolic-elliptic Keller--Segel system. In particular, solutions globally exist in both cases as...
Blowup of solutions to a diffusive aggregation model (2009)
Biler, Piotr, Karch, Grzegorz, Laurençot, Philippe
The nonexistence of global in time solutions is studied for a class of aggregation equations involving L\'evy diffusion operators and general interaction kernels.
Nonlinear diffusion of dislocation density and self-similar solutions (2009)
Biler, Piotr, Karch, Grzegorz, Monneau, Régis
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations in crystals. The long time asymptotics of solutions is described by the self-similar profiles.
Nonlinear diffusion of dislocation density and self-similar solutions (2009)
Biler, Piotr, Karch, Grzegorz, Monneau, Régis
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations in crystals. The long time asymptotics of solutions is described by the self-similar profiles.
Biler, Piotr, Corrias, Lucilla, Dolbeault, Jean
In two space dimensions, the parabolic-parabolic Keller--Segel system shares many properties with the parabolic-elliptic Keller--Segel system. In particular, solutions globally exist in both cases as...
Biler, Piotr, Corrias, Lucilla, Dolbeault, Jean
In two space dimensions, the parabolic-parabolic Keller--Segel system shares many properties with the parabolic-elliptic Keller--Segel system. In particular, solutions globally exist in both cases as...
Nonlinear diffusion of dislocation density and self-similar solutions (2008)
Biler, Piotr, Karch, Grzegorz, Monneau, Regis
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
Blow up of solutions to generalized Keller--Segel model (2008)
The existence and nonexistence of global in time solutions is studied for a class of equations generalizing the chemotaxis model of Keller and Segel. These equations involve L\'evy diffusion...
Biler, Piotr, Brandolese, Lorenzo
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model,...
Biler, Piotr, Brandolese, Lorenzo
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model,...
Biler, Piotr, Brandolese, Lorenzo
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model,...
Biler, Piotr, Brandolese, Lorenzo
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model,...
Biler, Piotr, Brandolese, Lorenzo
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model,...
Piotr Biler, Jean Dolbeault, Maria J. Esteban
In this paper, we study type II Streater's models. These models describe the coupled evolution of the density of a cloud of particles in an external potential and a temperature, preserving the...
Piotr Biler, Maria J. Esteban, Peter A. Markowich, Tadeusz Nadzieja
Steady states for Streater's energy-transport models of self-gravitating particles
Piotr Biler, Maria J. Esteban, Peter A. Markowich, Tadeusz Nadzieja
Steady states for Streater's energy-transport models of self-gravitating particles
Piotr Biler, Jean Dolbeault, Maria J. Esteban
In this paper, we study type II Streater's models. These models describe the coupled evolution of the density of a cloud of particles in an external potential and a temperature, preserving the...
Steady states for Streater's energy-transport models of self-gravitating particles (2007)
Piotr Biler, Jean Dolbeault, Maria J. Esteban, Peter A. Markowich, Tadeusz Nadzieja
We review Streater's energy-transport models which describe the temporal evolution of the density and temperature of a cloud of gravitating particles, coupled to a mean field Poisson equation....
Global existence versus blow up for some models of interacting particles (2006)
Biler, Piotr, Brandolese, Lorenzo
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion...
Global existence versus blow up for some models of interacting particles (2006)
Biler, Piotr, Brandolese, Lorenzo
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion...
Global existence versus blow up for some models of interacting particles (2006)
Biler, Piotr, Brandolese, Lorenzo
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion...
Global existence versus blow up for some models of interacting particles (2006)
Biler, Piotr, Brandolese, Lorenzo
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion...
Global existence versus blow up for some models of interacting particles (2006)
Biler, Piotr, Brandolese, Lorenzo
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion...
The Erwin, Schrödinger International Boltzmanngasse, Piotr Biler, Jean Dolbeault, Piotr Biler, Jean Dolbeault
Available via anonymous ftp or gopher from FTP.ESI.AC.AT
Piotr Biler, Jean Dolbeault, Jean Dolbeault Ceremade
Long time behavior of solutions to Nernst-Planck and Debye-H"uckel drift-diffusion systems
Large time asymptotics of nonlinear driftdiffusion systems with Poisson coupling (1999)
Piotr Biler, Jean Dolbeault, Peter A. Markowich
We study the asymptotic behavior as t!+1 of a system of densities of charged particles satisfying nonlinear drift-diffusion equations coupled by a damped Poisson equation for the drift-potential. 1...
Large time asymptotics of nonlinear drift-diffusion systems with Poisson coupling (1999)
Piotr Biler, Jean Dolbeault, Peter A. Markowich
We study the asymptotic behavior as ... of a system of densities of charged particles satisfying nonlinear drift-diffusion equations coupled by a damped Poisson equation for the drift-potential. In...
Long time behavior of solutions to Nernst-Planck and Debye-Huckel drift-diffusion systems (1999)
Piotr Biler Mathematical, Piotr Biler, Jean Dolbeault
We study the convergence rates of solutions to drift-diffusion systems (arising from plasma, semiconductors and electrolytes theories) to their self-similar or steady states. This analysis involves...
Long time behavior of solutions to Nernst-Planck and Debye-Hückel drift-diffusion systems (1999)
We study the convergence rates of solutions to drift-diffusion systems (arising from plasma, semiconductors and electrolytes theories) to their self-similar or steady states. This analysis involves...
Problems and Examples in Differential Equations (1992)
Biler, Piotr, Nadzieja, Tadeusz
0-8247-8637-8
Blowup of solutions to a diffusive aggregation model (0000)
The nonexistence of global in time solutions is studied for a class of aggregation equations involving Lévy diffusion operators and general interaction kernels.
Blowup of solutions to a diffusive aggregation model
The nonexistence of global in time solutions is studied for a class of aggregation equations involving Lévy diffusion operators and general interaction kernels.