Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a "Viscosity" Term. (18th September 2013)

• Record Type: Journal Article
• Authors: Kikuchi, Koji
• Other Names: Kowalewski Adam Academic Editor.
• Is Part Of: Journal of calculus of variations. Volume 2013(2013)
• Publication Date: 2013-09-18
• Subjects: Calculus of variations -- Periodicals; Calculus of variations; Electronic journals; Periodicals; 515.64
• DOI: 10.1155/2013/936915
• Languages: English
• ISSNs: 2314-6613

Abstract

Abstract : A nonlinear equation of motion of vibrating membrane with a "viscosity" term is investigated. Usually, the term- Δ u t is added, and it is well known that this equation is well posed in the space ofW 1, 2 functions. In this paper, the viscosity term is changed to- ( div ( ∇ u / 1 + | ∇ u | 2 ) ) t, and it is proved that if initial data is slightly smooth (but belonging toW 2, 2 is sufficient), then a weak solution exists uniquely in the space of BV functions.