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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00587705" target="_blank" >RIV/67985840:_____/24:00587705 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00208-023-02733-4" target="_blank" >https://doi.org/10.1007/s00208-023-02733-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00208-023-02733-4" target="_blank" >10.1007/s00208-023-02733-4</a>

Result language
angličtina
Original language name
On growth and instability for semilinear evolution equations: an abstract approach
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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