# 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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