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Evolution families and maximal regularity for systems of parabolic equations. (English) Zbl 1377.35130

Summary: 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.

MSC:

35K40 Second-order parabolic systems
35K90 Abstract parabolic equations
42B37 Harmonic analysis and PDEs
34G10 Linear differential equations in abstract spaces
35B65 Smoothness and regularity of solutions to PDEs
42B15 Multipliers for harmonic analysis in several variables
47D06 One-parameter semigroups and linear evolution equations
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