### Evolution families and maximal regularity for systems of parabolic equations

#### Abstract

In this paper, we prove maximal $L^p$-regularity for a system of parabolic PDEs, where the elliptic operator $A$ has coefficients which depend on time in a measurable way and are continuous in the space variable. The proof is based on operator-theoretic methods and one of the main ingredients in the proof is the construction of an evolution family on weighted $L^q$-spaces.

#### Article information

Source
Adv. Differential Equations, Volume 22, Number 3/4 (2017), 169-190.

Dates
First available in Project Euclid: 18 February 2017