Asymptotic behaviour of nonlinear wave equations in a noncylindrical domain becoming unbounded
Texas State University, Department of Mathematics
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.
Nonlinear wave equation, Asymptotic behaviour in time, Noncylindrical domains
Aibeche, A., Hadi, S., & Sengouga, A. (2017). Asymptotic behaviour of nonlinear wave equations in a noncylindrical domain becoming unbounded. <i>Electronic Journal of Differential Equations, 2017</i>(288), pp. 1-15.