Abstract
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 \( \mathbb {R}^N \). 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.
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Acknowledgements
This work is supported by the Van Lang University. We confirm that the third author Anh Tuan Nguyen is the corresponding author of this paper. We thank the anonymous reviewer for his/her careful reading of our manuscript and his/her insightful comments and suggestions.
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Tuan, N.H., Au, V.V. & Nguyen, A.T. Mild solutions to a time-fractional Cauchy problem with nonlocal nonlinearity in Besov spaces. Arch. Math. 118, 305–314 (2022). https://doi.org/10.1007/s00013-022-01702-8
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DOI: https://doi.org/10.1007/s00013-022-01702-8