Existence and uniqueness of travelling waves in a reaction-diffusion equation with combustion nonlinearity. (English) Zbl 0727.35070
We prove the existence of travelling wave solutions in a reaction- diffusion equation with general periodic diffusion coefficients, zero drift coefficients, and combustion nonlinearity in \({\mathbb{R}}^ n\), \(n\geq 1\). We also prove monotonicity and uniqueness of travelling wave solutions under an additional assumption on the combustion nonlinearity.
Reviewer: X.Xin (Berkeley)
MSC:
35K57 | Reaction-diffusion equations |