Work

On growth and instability for semilinear evolution equations: an abstract approach

Year: 2023

Type: article

Abstract: We propose a new approach to the study of (nonlinear) growth and instability for semilinear abstract evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of linear evolution equations can be treated as linear ones as far as the growth of their solutions is concerned. We obtain exponential lower bounds of solutions for initial values from a dense set in resolvent or spectral terms. The abstract results are applied, in particular, to the study of energy growth for semilinear backward damped wave equations.

Source: Mathematische Annalen

DOI: 10.1007/s00208-023-02733-4

Authors: Vladimir Müller, Roland Schnaubelt, Yuri Tomilov