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2005 Existence and regularity results for solutions to nonlinear parabolic equations
Nathalie Grenon, Anna Mercaldo
Adv. Differential Equations 10(9): 1007-1034 (2005).

Abstract

In this paper we prove some existence and regularity results for solutions to a class of nonlinear parabolic equations whose prototype is $$\left\{\begin{array}{lll} \displaystyle\frac{\partial u}{\partial t}-\Delta_p u=f(x,t) &\mbox{ in }Q,\cr u(x,0)=0 &\mbox{ in } \Omega,\cr u(x,t)=0 &\mbox{ on } \Gamma, \end{array}\right. $$ \noindent where $\Omega$ is a bounded open subset of ${{\mathbb R}^ N} $, $N\ge 2$, $Q$ is the cylinder $\Omega \times ]0,T[$, $T>0$, $\Gamma$ the lateral surface $\partial\Omega\times ]0,T[$, $\bigtriangleup _p$ is the so-called $p-$Laplace operator, $ p>1 $ and $f$ belongs to some space $ L^r (0,T;L^q(\Omega )),$ $r\geq 1$, $q\geq 1$.

Citation

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Nathalie Grenon. Anna Mercaldo. "Existence and regularity results for solutions to nonlinear parabolic equations." Adv. Differential Equations 10 (9) 1007 - 1034, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1100.35052
MathSciNet: MR2161757

Subjects:
Primary: 35K55
Secondary: 35B65, 35D10, 35K20

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 9 • 2005
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