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

TL;DR

This paper investigates $L^p$-maximal regularity for non-autonomous linear evolution equations with right multiplicative perturbations, focusing on operators arising from sesquilinear forms in Hilbert spaces and applications to 1D parabolic PDEs.

Contribution

It establishes $L^p$-maximal regularity results for non-autonomous equations with bounded invertible perturbations, extending previous theory to include right multiplicative perturbations.

Findings

Results apply to operators from sesquilinear forms in Hilbert spaces.

Provides maximal regularity for 1D parabolic equations.

Extends existing theory to non-autonomous right multiplicative perturbations.

Abstract

This paper is devoted to the study of $L^p$-maximal regularity for non-autonomous linear evolution equations of the form \begin{equation*}\label{Multi-pert1-diss-non} \dot u(t)+A(t)B(t)u(t)=f(t)\ \ 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.