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 |
URI: | http://hdl.handle.net/2003/34963 http://dx.doi.org/10.17877/DE290R-17011 |
Issue Date: | 2016-03 |
Appears in Collections: | Lehrstuhl I: Analysis |
Files in This Item:
File | Description | Size | Format | |
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Dissertation.pdf | DNB | 1.01 MB | Adobe PDF | View/Open |
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