DOCUMENTA MATHEMATICA, Vol. 19 (2014), 1141-1153

Vitaly Volpert, Vitali Vougalter

Existence of Stationary Pulses for Nonlocal Reaction-Diffusion Equations

A nonlocal reaction-diffusion equation and a system of equations from population dynamics are considered on the whole axis. Existence of solutions in the form of stationary pulses is proved by a perturbation method. It is based on spectral properties of the linearized operators and on the implicit function theorem.

2010 Mathematics Subject Classification: 35K57, 35A16, 92D15

Keywords and Phrases: reaction-diffusion equation, existence of pulse solutions, perturbation methods

Full text: dvi.gz 21 k, dvi 51 k, ps.gz 219 k, pdf 130 k.