Differential and Integral Equations

Quasilinear parabolic integro-differential equations with nonlinear boundary conditions

Rico Zacher

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35K60: Nonlinear initial value problems for linear parabolic equations 35K65: Degenerate parabolic equations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]


Zacher, Rico. Quasilinear parabolic integro-differential equations with nonlinear boundary conditions. Differential Integral Equations 19 (2006), no. 10, 1129--1156. https://projecteuclid.org/euclid.die/1356050312

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