Averaging of the periodic by time boundary value problem for the nonlinear wave equation in a perforated domain (Q2735869)
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scientific article; zbMATH DE number 1641377
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Averaging of the periodic by time boundary value problem for the nonlinear wave equation in a perforated domain |
scientific article; zbMATH DE number 1641377 |
Statements
14 November 2001
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periodic in time Dirichlet problems
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infinitely increasing quantity of infinitesimal holes
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Averaging of the periodic by time boundary value problem for the nonlinear wave equation in a perforated domain (English)
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It is studied the averaging of the periodic in time Dirichlet problems for the wave equations with additional power nonlinearity depending on the time derivative of the solution in a bounded domain with infinitely increasing quantity of infinitesimal holes whose asymptotic behaviour is described formally by means of the hypotheses of D. Cioranescu and F. Murat. A weak convergence of sequences of solutions of problems under consideration and their time derivatives in corresponding spaces is established. The periodic in time boundary value problem for the limit function is constructed.
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