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2007 Semilinear parabolic equations in $L^1(\Omega)$
Gabriella Di Blasio
Adv. Differential Equations 12(12): 1393-1414 (2007).

Abstract

This paper studies existence, regularity and continuous dependence upon the data of solutions to parabolic semilinear problems of the form: $u'(t)=Au(t) +g[u(t)]$, $u(0)=u_0$. Here, $A:D(A)\to X$ generates an analytic semigroup on a Banach space $X$ and $g:D(g)\to X$. It is assumed that $D(g)$ contains a certain interpolation space of $X$ and $D(A)$; this will allow to treat parabolic partial semilinear problems in the cases where the nonlinear term depends also on the gradient of $u$.

Citation

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Gabriella Di Blasio. "Semilinear parabolic equations in $L^1(\Omega)$." Adv. Differential Equations 12 (12) 1393 - 1414, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1152.35067
MathSciNet: MR2382730

Subjects:
Primary: 35K55
Secondary: 34G20, 35K20, 35K90

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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