Electron. J. Diff. Equ., Vol. 2014 (2014), No. 81, pp. 1-9.

Convergence to equilibrium of relatively compact solutions to evolution equations

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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