On the two dimensional wave equation in time-dependent domains. - Lamrad, Haroun (Faculty of Mathematics and computer sciences Department of Mathematics - Option : PDEs and application, 2021)
We consider the 2-dimensional wave equation in non-cylindrical domains, i.e. domains depending on time. We rst use a penalization method depending on a parameter ". The obtained problem is a wave equation, posed in a cylindrical domain, with a penalized weak damping term. If the domain is expanding with time, we show that the solution of the penalized problem converges to the solution of the original problem, as " ! 0. Finally, to obtain a numerical approximation of solutions, we combine this penalization method with an explicit nite di erences approach.
Keywords: Wave equation, non-cylindrical domains, penalization method, nite di erences.