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A singular perturbation problem for nonlinear damped hyperbolic equations

Published online by Cambridge University Press:  14 November 2011

Piotr Biler
Piotr Biler
Affiliation:
Mathematical Institute, University of Wroclaw, pi. Grunwaldzki 2/4, 50-384 Wrocław, Poland Laboratoire d'Analyse Numérique, Université de Paris-Sud, bât. 425, 91405 Orsay, France
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Synopsis

We consider damped nonlinear hyperbolic equations utt + Aut + αAu + βA2u + G(u) = 0, where A is a positive operator and G is the Gateaux derivative of a convex functional. We examine the asymptotic behaviour of solutions and the convergence of strong solutions to these equations when the parameter β tends to zero.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 21 - 31
Copyright
Copyright © Royal Society of Edinburgh 1989

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