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
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