The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces. (22nd June 2015) - Wu, Yun; Liu, Zhengrong; Zhang, Xiang
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.