Abstract
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 spaceBp,rs(T). Furthermore, we study the continuity of the solution map for this equation inB2,rs(T). Our work improves some earlier results.
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