Convergence to equilibrium for solutions of an abstract wave equation with general damping function

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10335074" target="_blank" >RIV/00216208:11320/16:10335074 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jde.2015.10.003" target="_blank" >http://dx.doi.org/10.1016/j.jde.2015.10.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2015.10.003" target="_blank" >10.1016/j.jde.2015.10.003</a>

Result language
angličtina
Original language name
Convergence to equilibrium for solutions of an abstract wave equation with general damping function
Original language description
We prove convergence to a stationary solution as time goes to infinity of solutions to abstract nonlinear wave equation with general damping term and gradient nonlinearity, provided the trajectory is precompact. The energy is supposed to satisfy a Kurdyka-Lojasiewicz gradient inequality. Our aim is to formulate conditions on the function g as general as possible when the damping is a scalar multiple of the velocity, and this scalar depends on the norm of the velocity, g(vertical bar u(t)vertical bar)u(t). These turn out to be estimates and a coupling condition with the energy but not global monotonicity. When the damping is more general, we need an angle condition.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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