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2006 Quasilinear parabolic integro-differential equations with nonlinear boundary conditions
Rico Zacher
Differential Integral Equations 19(10): 1129-1156 (2006).

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.

Citation

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Rico Zacher. "Quasilinear parabolic integro-differential equations with nonlinear boundary conditions." Differential Integral Equations 19 (10) 1129 - 1156, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.45015
MathSciNet: MR2278673

Subjects:
Primary: 35K55
Secondary: 35K60 , 35K65 , 45K05

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 10 • 2006
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