The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces

الملخص EN

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 space B p , r s ( T ) .

Furthermore, we study the continuity of the solution map for this equation in B 2 , r s ( T ) .

Our work improves some earlier results.