Preprint series: 06-05 , Reports on Analysis

MSC:

45K05 Integro-partial differential equations

45G05 Singular nonlinear integral equations

Abstract: We study the $L_p$-theory of a class of quasilinear parabolic
partial integro-differential equations with nonlinear boundary
conditions. The main objective here is to prove existence and
uniqueness of local (in time) strong solutions of these problems.
Our approach relies on linearization and the contraction mapping
principle. To make this work we establish optimal regularity
estimates of type $L_p$ for associated linear problems with
inhomogeneous boundary data, using here recent results on maximal
$L_p$-regularity for abstract parabolic Volterra equations.

Keywords: maximal regularity, quasilinear problem, nonlinear boundary condition, parabolic Volterra equation, integro-differential equation

Upload: 2006-05-16