Stability of perturbed nonlinear parabolic equations with Sturmian property (Q1888362)

In an abstract setting, the authors study the stability of an equilibrium \(f^*\) of an autonomous dynamical system under asymptotically small perturbations of \(f^*\), and show that such stability takes place if the domain of attraction for \(f^*\) contains a one-parameter ordered family (see the paper for details and the corresponding order relation). In the stability analysis they make use of a so-called \(S\)-relation inherited from the Sturmian zero set properties for linear parabolic equations. As application they show stability of the self-similar blow-up behavior for the porous medium equation, the \(p\)-Laplacian equation and the dual porous medium equation in \({\mathbb R}\) with nonlinear lower-order perturbation.