Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 52, Number 4 (2000), 741-766.
An analysis of the nonlinear equation of motion of a vibrating membrane in the space of BV functions
In this article the nonlinear equation of motion of vibrating membrane 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 and that, if 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.
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 741-766.
First available in Project Euclid: 10 June 2008
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Zentralblatt MATH identifier
Primary: 35L70: Nonlinear second-order hyperbolic equations 49J40: Variational methods including variational inequalities [See also 47J20] 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]
KIKUCHI, Koji. An analysis of the nonlinear equation of motion of a vibrating membrane in the space of BV functions. J. Math. Soc. Japan 52 (2000), no. 4, 741--766. doi:10.2969/jmsj/05240741. https://projecteuclid.org/euclid.jmsj/1213107108