Stability of travelling waves with noncritical speeds for double degenerate Fisher-type equations
This article focuses on a Fisher-type equation where the classical nonlinearity \(u\,(1-u)\) is replaced by \(u^p\,(1-u)^q\), \(p,q>1\). For this type of equation it is known that there exists a critical speed \(c^*\) such that there exist traveling wave solutions for any speed \(c\geq c^*\) connecting the solutions \(u=0\) and \(u=1\). Traveling waves with \(c>c^*\) are shown to be exponentially stable in certain exponentially weighted spaces and locally algebraically/exponentially stable in certain polynomially/exponentially weighted spaces.
scientific article; zbMATH DE number 5302656