Thermal waves in absorbing media (Q1116018)

Starting from the equation \(u_ t=a(u^ m)_{xx}-b u^ n\) with \(a,b>0\), \(u\geq 0\) and m,n real numbers, the authors study travelling-wave solutions (TWS) i.e. solutions of the form \(u(x,t)=\Phi (ct-x)\) with \(\Phi\geq 0\), \(\Phi\) (s)\(\to 0\) as \(s\to -\infty\). They obtain existence and uniqueness up to translation of TWS for given values of c (depending on n and m) and study their asymptotic behavior.