Tomas Barta
Abstract:
We prove convergence to equilibrium for relatively compact solutions
to an abstract evolution equation satisfying energy estimates near
the omega-limit set. These energy estimates generalize Lojasiewicz
and Kurdyka-Lojasiewicz-Simon gradient inequalities.
We apply the abstract results to several ODEs and PDEs of first and
second order.
Submitted October 29, 2013. Published March 21, 2014.
Math Subject Classifications: 35R20, 35B40, 34D05, 34G20.
Key Words: Convergence to equilibrium; gradient system;
Kurdyka-Lojasiewicz gradient inequality; gradient-like system.
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Tomas Barta Department of Mathematical Analysis Faculty of Mathematics and Physics, Charles University Sokolovska 83, 186 75 Prague 8, Czech Republic email: barta@karlin.mff.cuni.cz |
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