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Abstract parabolic systems and regularized semigroups. (English) Zbl 0915.47036

Summary: The main purpose of this paper is to obtain the wellposedness of abstract parabolic systems in the sense of Petrovsij and Shilov under sharper conditions by using regularized semigroups. We also consider these systems with time-dependent coefficients, and give the applications to the corresponding parabolic systems on many function spaces.

MSC:

47F05 General theory of partial differential operators
35K10 Second-order parabolic equations
47D06 One-parameter semigroups and linear evolution equations
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