Journal of Operator Theory

Volume 74, Issue 2, Fall 2015 pp. 391-415.

On the right multiplicative perturbation of non-autonomous $L^p$-maximal regularity

Authors: Bjorn Augner (1), Birgit Jacob (2), and Hafida Laasri (3)
Author institution: (1) University of Wuppertal, Work Group Functional Analysis, 42097 Wuppertal, Germany
(2) University of Wuppertal, Work Group Functional Analysis, 42097 Wuppertal, Germany
(3) University of Hagen, Faculty of Mathematics and Computer Science, 58084 Hagen, Germany

Summary: This paper is devoted to the study of $L^p$-maximal regularity for non-autonomous linear evolution equations of the form \begin{equation*} \dot u(t)+A(t)B(t)u(t)=f(t)\quad t\in[0,T], u(0)=u_0, \end{equation*} where $\{A(t), t\in [0,T]\}$ is a family of linear unbounded operators whereas the operators $\{B(t), t\in [0,T]\}$ are bounded and invertible. In the Hilbert space situation we consider operators $A(t), t\in[0,T],$ which arise from sesquilinear forms. The obtained results are applied to parabolic linear differential equations in one spatial dimension.

DOI: http://dx.doi.org/10.7900/jot.2014jul31.2064
Keywords: $L^p$-maximal regularity, non-autonomous evolution equation, general parabolic equation

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