Mild solutions to a time-fractional Cauchy problem with nonlocal nonlinearity in Besov spaces

In this paper, we aim to study a time-fractional Cauchy problem for a heat equation with a nonlocal nonlinearity driven by simulation problems arising in populations, and biological mathematics. Using the Banach fixed-point argument, we investigate the existence and uniqueness of mild solutions in B...

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Bibliographic Details
Published inArchiv der Mathematik Vol. 118; no. 3; pp. 305 - 314
Main Authors Tuan, Nguyen Huy, Au, Vo Van, Nguyen, Anh Tuan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2022
Springer Nature B.V
Subjects
Cauchy problems
Dirichlet problem
Function space
Mathematics
Mathematics and Statistics
Nonlinearity
Thermodynamics
35K20
35R11
Time-fractional Cauchy problem
Nonlocal nonlinearity
Besov spaces
Well-posedness
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Summary:In this paper, we aim to study a time-fractional Cauchy problem for a heat equation with a nonlocal nonlinearity driven by simulation problems arising in populations, and biological mathematics. Using the Banach fixed-point argument, we investigate the existence and uniqueness of mild solutions in Besov spaces defined on an open subset of R N . The key tools of our method are some linear estimates of the heat semigroup generated by the Dirichlet Laplacian and techniques of the M-Wright function. Some embeddings are also used for our proofs.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-022-01702-8