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.
Koji KIKUCHI. "An analysis of the nonlinear equation of motion of a vibrating membrane in the space of BV functions." J. Math. Soc. Japan 52 (4) 741 - 766, October, 2000. https://doi.org/10.2969/jmsj/05240741