Asymptotic behaviour of nonlinear wave equations in a noncylindrical domain becoming unbounded
Aissa Aibèche, Sara Hadi, Abdelmouhcene Sengouga · DOAJ (DOAJ: Directory of Open Access Journals) · 2017
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.