Publication: Travelling wave solutions to a semilinear diffusion system
No Thumbnail Available
Full text at PDC
Publication Date
1990-01
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Citations
Exportar
Abstract
We consider the semilinear system (S) ut−uxx+vp=0, vt−vxx+uq=0(−∞<x<+∞,t>0) with p>0 and q>0. We seek nonnegative and nontrivial travelling wave solutions to (S): u(x,t)=φ(ct−x), v(x,t)=ψ(ct−x) possessing sharp fronts, i.e., such that φ(ξ)=ψ(ξ)=0 for ξ≤ξ0 and some finite ξ0, which after a phase shift can always be assumed to be located at the origin. These solutions are called finite travelling waves (FTW). Here we show that if pq<1, for any real c there exists an FTW that is unique up to phase translations and unbounded, whereas no FTW exists if pq≥1. The asymptotic wave profiles near the front as well as far from it are also determined.