Table of Contents
Journal of Calculus of Variations
Volume 2013 (2013), Article ID 936915, 11 pages
http://dx.doi.org/10.1155/2013/936915
Research Article

Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term

Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan

Received 30 April 2013; Accepted 11 July 2013

Academic Editor: Adam Kowalewski

Copyright © 2013 Koji Kikuchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A nonlinear equation of motion of vibrating membrane with a “viscosity” term is investigated. Usually, the term is added, and it is well known that this equation is well posed in the space of functions. In this paper, the viscosity term is changed to , and it is proved that if initial data is slightly smooth (but belonging to is sufficient), then a weak solution exists uniquely in the space of BV functions.