Aissa Aibeche, Sara Hadi, Abdelmouhcene Sengouga
Abstract:
We study the asymptotic behaviour for the solution of nonlinear wave
equations in a noncylindrical domain, becoming unbounded in some directions,
as the time t goes to infinity. If the limit of the source term is
independent of these directions and t, the wave converges to the solution
of an elliptic problem defined on a lower dimensional domain. The rate of
convergence depends on the limit behaviour of the source term and on the
coefficient of the nonlinear term.
Submitted August 7, 2017. Published November 21, 2017.
Math Subject Classifications: 35B35, 35B40, 35L70.
Key Words: Nonlinear wave equation; asymptotic behaviour in time;
noncylindrical domains
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Aissa Aibeche Department of Mathematics University Setif 1 Route de Scipion, 19000 Setif, Algeria email: aibeche@univ-setif.dz |
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| Sara Hadi Department of Mathematics University Setif 1 Route de Scipion, 19000 Setif, Algeria email: sarra_math@yahoo.fr | |
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Abdelmouhcene Sengouga Laboratory of Functional Analysis and Geometry of Spaces University of M'sila 28000 M'sila, Algeria email: amsengouga@gmail.com |
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