Journal of the Mathematical Society of Japan

An analysis of the nonlinear equation of motion of a vibrating membrane in the space of BV functions

Koji KIKUCHI

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Abstract

In this article the nonlinear equation of motion of vibrating membrane utt-div{1+|Vu|2-1Vu}=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.

Article information

Source
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 741-766.

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107108

Digital Object Identifier
doi:10.2969/jmsj/05240741

Mathematical Reviews number (MathSciNet)
MR1774628

Zentralblatt MATH identifier
0964.35101

Subjects
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]

Keywords
Hyperbolic equations BV functions Rothe's method direct variational method varifolds

Citation

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


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