American Institute of Mathematical Sciences

June  2012, 5(3): 567-580. doi: 10.3934/dcdss.2012.5.567

Some singular perturbations results for semilinear hyperbolic problems

 1 University of Zürich, Institute of Mathematics, Winterthurerstrasse 190, CH-8057 Zurich 2 Department of Mathematics, University of M’sila, BP:166, 28000, M’sila, Algeria

Received  August 2010 Revised  December 2010 Published  October 2011

This paper is concerned with the asymptotic behaviour of the solutions of some semilinear hyperbolic problems. Using the monotonicity hypothesis, convergence results are shown in different spaces depending on the derivative directions of an arbitrary domain $\Omega .$ Some improvements are established when $\Omega$ is a cylinder.
Citation: Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567
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