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

Convergence to equilibrium of relatively compact solutions to evolution equations

Tomas Barta

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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