Abstract
This paper contains some existence and uniqueness results for the strict and classical solutionsu : [0,T] →E of the non-autonomous evolution equationu 1(t)=Λ(t)u(t)+f(t) in a Banach spaceE under the classical Tanabe-Sobolevski assumptions. These results do not require use of the fundamental solution and give new information about the hölder-regularity of the solutions.
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Work done as a member of G.N.A.F.A. of C.N.R.
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da Prato, G., Sinestrari, E. Hölder regularity for non-autonomous abstract parabolic equations. Israel J. Math. 42, 1–19 (1982). https://doi.org/10.1007/BF02765006
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DOI: https://doi.org/10.1007/BF02765006