Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

08-043 Jens Rottmann-Matthes.
Spectral Analysis of Coupled Hyperbolic-Parabolic Systems on Finite and Infinite Intervals

In many applied problems in biology, physics or chemistry traveling waves arise as solutions of systems of partial differential equations of the form

A traveling wave has the special property that it is constant if one looks at it in a comoving frame. More precisely this means if U is a traveling wave solution of (1) with speed c, the function is a steady state of the transformed PDE

For the stability analysis of traveling waves it is important to know where the point spectrum of the linearized right hand side of (2) lies. We will show how this can be approximated by computing the spectrum of boundary value problems.