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2000 Non-autonomous Miyadera perturbations
Abdelaziz Rhandi, Frank Räbiger, Roland Schnaubelt, Jürgen Voigt
Differential Integral Equations 13(1-3): 341-368 (2000). DOI: 10.57262/die/1356124303


We consider time dependent perturbations $B(t)$ of a non--autonomous Cauchy problem $\dot{v}(t)=A(t)v(t)$ $(CP)$ on a Banach space $X$. The existence of a mild solution $u$ of the perturbed problem is proved under Miyadera type conditions on $B(\cdot)$. In the parabolic case and $X=L^d(\Omega)$, $1 < d < \infty$, we show that $u$ is differentiable a.e. and satisfies $\dot{u}(t)=(A(t)+B(t))u(t)$ for a.e. $t$. Our approach uses perturbation results due to one of the authors, [29], and S. Monniaux and J. Prüß, [14], which are applied to the evolution semigroup induced by the evolution family related to $(CP)$. As an application we obtain solutions of a second order parabolic equation with singular lower order coefficients.


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Abdelaziz Rhandi. Frank Räbiger. Roland Schnaubelt. Jürgen Voigt. "Non-autonomous Miyadera perturbations." Differential Integral Equations 13 (1-3) 341 - 368, 2000.


Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0980.34056
MathSciNet: MR1811962
Digital Object Identifier: 10.57262/die/1356124303

Primary: 34G10
Secondary: 35K10 , 35K90 , 47A55 , 47D06

Rights: Copyright © 2000 Khayyam Publishing, Inc.

Vol.13 • No. 1-3 • 2000
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