The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces. (22nd June 2015)

• Record Type: Journal Article
• Authors: Wu, Yun; Liu, Zhengrong; Zhang, Xiang
• Other Names: Keyantuo Valentin Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-06-22
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/862593
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type:∂ t u + f ( u ) ∂ x u + F ( u ) = 0, x ∈ T = R / 2 π Z, t ∈ R + . Under some conditions, we prove that this equation is locally well-posed in Besov spaceB p, r s ( T ) . Furthermore, we study the continuity of the solution map for this equation inB 2, r s ( T ) . Our work improves some earlier results.