Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term
Author
Source
Journal of Calculus of Variations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-18
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
A nonlinear equation of motion of vibrating membrane with a “viscosity” term is investigated.
Usually, the term -Δut is added, and it is well known that this equation is well posed in the space of W1,2 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 to W2,2 is sufficient), then a weak solution exists uniquely in the space of BV functions.
American Psychological Association (APA)
Kikuchi, Koji. 2013. Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term. Journal of Calculus of Variations،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-509613
Modern Language Association (MLA)
Kikuchi, Koji. Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term. Journal of Calculus of Variations No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-509613
American Medical Association (AMA)
Kikuchi, Koji. Existence and Uniqueness of a Solution in the Space of BV Functions to the Equation of a Vibrating Membrane with a “Viscosity” Term. Journal of Calculus of Variations. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-509613
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509613
