Quasilinear Evolutionary Equations and Continuous Interpolation Spaces;Research rept

摘要

In this paper we analyze the abstract parabolic evolutionary equations D (sup alpha) (sub t) (u - x ) + A(u)u=f(u)+h(t), u(0)=x, In continuous interpolation spaces allowing a singularity s t arrow ). We first give a treatment of fractional derivatives in the spaces L(sup p) ((0,T); X) and then consider tese derivatives in spaces of continuous functions having (at most) a prescrbed singularity as t arrow 0. The corresponding trace spaces are characterized and the dependence on alpha is demonstrated.