On maximal solution to a degenerate parabolic equation involving in time fractional derivative
Keywords:
degenerate parabolic equation, fractional integrodifferential equation, mild solution, maximal solutionAbstract
In this paper, we consider a degenerate parabolic equation associated with Caputo derivative. Our problem is studied in the unbounded domain and the nonlocal initial condition. Under some suitable conditions of the input data, we show the local existence of the mild solution. Then we show the continuation of the mild solution. We also claim the maximal mild solution. The main analysis in the current paper is based on some estimations of resolvent theory combined with many complex valuations on solutions operators in Banach spaces.
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Copyright (c) 2023 Bui Dai Nghia; Nguyen Hoang Luc (Corresponding Author); Xiaolan Qin, Yan Wang
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Accepted 2023 May 04
Published 2023 May 08