Authors: Badke, Sven
Title: Traveling wave solutions of reaction-diffusion equations with x-dependent combustion type nonlinearities
Language (ISO): en
Abstract: We investigate the existence and uniqueness of traveling wave solutions of the reaction-diffusion equation in periodic heterogeneous media. The reaction-diffusion equation is considered in nondivergence form with no first order term. Our traveling wave problem is considered in similar form in [1] by Xin in the special case that the reaction-term is given by a combustion nonlinearity ƒ = ƒ(u). We prove the existence of traveling wave solutions in case of a class of nonlinearities ƒ = ƒ(x, u), which are a generalization of a combustion nonlinearity. In particular, ƒ is allowed to depend explicitly on x. In case of an additional assumption on ƒ, we also prove a monotonicity result and a uniqueness result. References [1] X. Xin. Existence and uniqueness of travelling waves in a reaction-diffusion equation with combustion nonlinearity. Indiana Univ. Math. J., 40(3):985–1008, 1991.
Subject Headings: Traveling wave
Reaction-diffusion equation
Combustion nonlinearity
Issue Date: 2016-03
Appears in Collections:Lehrstuhl I: Analysis

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