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

Autor:	Müller, Vladimir, Schnaubelt, Roland, Tomilov, Yuri
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematics - Functional Analysis 35B40 37L15 47H08 47J35
Druh dokumentu:	Working Paper
Popis:	We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation 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 if, e.g., the resolvent of the generator is unbounded on a vertical line in the right halfplane. Comment: This is a version of the paper to appear in Mathematische Annalen
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2211.15121 Zobrazit plný text záznamu View this record from Arxiv