| Travelling-Wave Solutions for Reaction-Diffusion-Convection Systems (2007) | |||||||||||||
Abstract | |||||||||||||
| We prove the existence of travelling-wave solutions of the parabolic system @u @t = A @ 2 u @x 2 + G(u; @u @x ) @u @x + f(u); where the reaction term f is of `bistable' type and the convection term G is a nonlinear matrix-valued function satisfying certain growth conditions. A monotone travelling wave connecting two equilibria is shown to exist using degree theory and a homotopy to a convectionless system previously studied by Vol'pert, Vol'pert and Vol'pert. Their theory of reaction-diffusion systems is thereby extended to include nonlinear convection terms. R'esum'e Nous prouvons l'existence d'une onde progressive du syst`eme parabolique @u @t = A @ 2 u @x 2 + G(u; @u @x ) @u @x + f(u): Ici le terme de r'eaction f est `bistable', et le terme de convection G est une fonction matricielle non lin'eaire qui satisfait une condition de croissance. L'existence d'une onde progressive monotone entre deux equilibres est demontr'ee par la theorie du degr'e. On homotope `a un... | |||||||||||||
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