Geodesic
Convergence to equilibrium of relatively compact solutions to evolution equations
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35R20, 35B40, 34D05, 34G20
Keywords: convergence to equilibrium, gradient system, Kurdyka-lojasiewicz gradient inequality, gradient-like system 
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     author = {Barta, Tomas},
     title = {Convergence to equilibrium of relatively compact solutions to evolution equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a110/}
}
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Barta, Tomas. Convergence to equilibrium of relatively compact solutions to evolution equations. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a110/