# American Institute of Mathematical Sciences

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

 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

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.
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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