On growth and instability for semilinear evolution equations: an abstract approach
Autor: | Müller, Vladimir, Schnaubelt, Roland, Tomilov, Yuri |
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Rok vydání: | 2022 |
Předmět: | |
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 |
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