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DISCRETE AND CONTINUOUS Website: http://aimSciences.org DYNAMICAL SYSTEMS
 

Summary: DISCRETE AND CONTINUOUS Website: http://aimSciences.org
DYNAMICAL SYSTEMS
Volume 15, Number 3, July 2006 pp. 921­938
ASYMPTOTIC SELECTION OF VISCOSITY EQUILIBRIA OF
SEMILINEAR EVOLUTION EQUATIONS BY THE
INTRODUCTION OF A SLOWLY VANISHING TERM
Felipe Alvarez
Departamento de Ingenier´ia Matem´atica
Centro de Modelamiento Matem´atico, Universidad de Chile
Av. Blanco Encalada 2120, 837-0459 Santiago, Chile
Alexandre Cabot
D´epartement de Math´ematiques, Universit´e de Limoges
123, avenue Albert Thomas, Limoges, France
(Communicated by Roger Temam)
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 station-
ary 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

  

Source: Alvarez, Felipe - Departamento de Ingeniería Matemática, Universidad de Chile

 

Collections: Mathematics; Engineering