On a Nonlinear Wave Equation Associated with Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters. (30th May 2011)

• Record Type: Journal Article
• Authors: Ngoc, Le Thi Phuong; Luan, Le Khanh; Thuyet, Tran Minh; Long, Nguyen Thanh
• Other Names: Jauberteau F. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2011(2011)
• Publication Date: 2011-05-30
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2011/625908
• Languages: English
• ISSNs: 2090-5564

Abstract

Abstract : A Dirichlet problem for a nonlinear wave equation is investigated. Under suitable assumptions, we prove the solvability and the uniqueness of a weak solution of the above problem. On the other hand, a high-order asymptotic expansion of a weak solution in many small parameters is studied. Our approach is based on the Faedo-Galerkin method, the compact imbedding theorems, and the Taylor expansion of a function.