An analysis of the nonlinear equation of motion of a vibrating membrane in the space of BV functions
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概要
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In this article the nonlinear equation of motion of vibrating membrane u<SUB>tt</SUB>-div{√{1+|∇ u|<SUP>2</SUP>}<SUP>-1</SUP>∇ u}=0 is discussed in the space of functions having bounded variation. Approximate solutions are constructed in Rothe's method. It is proved that a subsequence of them converges to a function u and that, if u satisfies the energy conservation law, then it is a weak solution in the space of functions having bounded variation. The main tool is varifold convergence.
- Mathematical Society of Japanの論文
- 2000-10-01
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