Asymptotic selection of viscosity equilibria of semilinear evolution equations by the introduction of a slowly vanishing term

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August 2006, 15(3): 921-938. doi: 10.3934/dcds.2006.15.921

Asymptotic selection of viscosity equilibria of semilinear evolution equations by the introduction of a slowly vanishing term

Felipe Alvarez ^1, and Alexandre Cabot ^2,

1.	Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, 837-0459 Santiago, Chile
2.	Département de Mathématiques, Université de Limoges, 123, avenue Albert Thomas, Limoges, France

Received April 2005 Revised November 2005 Published April 2006

Abstract
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The behavior at infinity is investigated of global solutions to some nonautonomous semilinear evolution equations with conservative and convex nonlinearities. It is proved that the trajectories converge to viscosity stationary solutions as time goes to infinity, that is, they evolve towards stationary solutions that are minimal with respect to a generalized viscosity criterion. Hierarchical viscosity selections and applications to specific nonlinear PDE are given.

Keywords: asymptotic behavior, Evolution equation, convergence, slow decay, selection principle., viscosity solution.

Mathematics Subject Classification: Primary: 35B40, 34G20; Secondary: 35K90, 37N4.

Citation: Felipe Alvarez, Alexandre Cabot. Asymptotic selection of viscosity equilibria of semilinear evolution equations by the introduction of a slowly vanishing term. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 921-938. doi: 10.3934/dcds.2006.15.921

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