Abstract
AbstractWe 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.
Funder
Narodowe Centrum Nauki
Grantová Agentura Ceské Republiky
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
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