On maximal solution to a degenerate parabolic equation involving in time fractional derivative

Authors

Bui Dai Nghia Department of Mathematics, Faculty of Science, Nong Lam University, Ho Chi Minh City, Vietnam https://orcid.org/0009-0003-8545-0683
Nguyen Hoang Luc Department of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam https://orcid.org/0000-0001-9664-6743
Xiaolan Qin School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China
Yan Wang School of Mathematical Science, Guizhou Normal University, Guiyang 550001, China

https://doi.org/10.61383/ejam.20231129

Keywords:

degenerate parabolic equation, fractional integrodifferential equation, mild solution, maximal solution

Abstract

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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Published

2023 May 08

How to Cite

[1]

B. Dai Nghia, N. Hoang Luc, X. Qin, and Y. Wang, “On maximal solution to a degenerate parabolic equation involving in time fractional derivative”, Electron. J. Appl. Math., vol. 1, no. 1, pp. 62–80, May 2023.