|Title:||Traveling wave solutions of reaction-diffusion equations with x-dependent combustion type nonlinearities|
|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  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  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|
|Appears in Collections:||Lehrstuhl I: Analysis|
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