期刊
MATHEMATICS IN ENGINEERING
卷 2, 期 4, 页码 584-597出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mine.2020026
关键词
obstacle problem; wave equation; one-dimensional
资金
- European Research Council (ERC) [721675]
Our goal is to review the known theory on the one-dimensional obstacle problem for the wave equation, and to discuss some extensions. We introduce the setting established by Schatzman within which existence and uniqueness of solutions can be proved, and we prove that (in some suitable systems of coordinates) the Lipschitz norm is preserved after collision. As a consequence, we deduce that solutions to the obstacle problem (both simple and double) for the wave equation have bounded Lipschitz norm at all times. Finally, we discuss the validity of an explicit formula for the solution that was found by Bamberger and Schatzman.
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