Differential and Integral Equations

Quasilinear parabolic integro-differential equations with nonlinear boundary conditions

Rico Zacher

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 $L_p$ type for associated linear problems with inhomogeneous boundary data, using here recent results on maximal $L_p$-regularity for abstract parabolic Volterra equations.

Article information

Source
Differential Integral Equations, Volume 19, Number 10 (2006), 1129-1156.

Dates
First available in Project Euclid: 21 December 2012