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2006, Volume 15, Issue 3: 921-938. Doi: 10.3934/dcds.2006.15.921
This issue Previous Article Dynamics of the degree six Landen transformation Next Article Periodic solutions for discrete convex Hamiltonian systems via Clarke duality

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

  • 2.

    Département de Mathématiques, Université de Limoges, 123, avenue Albert Thomas, Limoges

Received:  March 31, 2005
Revised:  October 31, 2005
Published:  August 2006
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    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35B40, 34G20; Secondary: 35K90, 37N40.

    Citation:
    shu

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