The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces - Yun Wu; Zhengrong Liu; Xiang Zhang (Journal of Function Spaces)
This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: ∂tu+f(u)∂xu+F(u)=0, x∈T=R/2πZ, t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov space Bp,rs(T). Furthermore, we study the continuity of the solution map for this equation in B2,rs(T). Our work improves some earlier results.