On the two dimensional wave equation in time-dependent domains.
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Date
2021
Authors
Journal Title
Journal ISSN
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Publisher
Faculty of Mathematics and computer sciences Department of Mathematics - Option : PDEs and application
Abstract
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.
Description
Keywords
Wave equation, non-cylindrical domains, penalization method, nite di erences.