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

Nguyen Huy TuanVo Van AuAnh Tuan Nguyen2022-10-252022-10-252022https://repository.vlu.edu.vn/handle/123456789/30310.1007/s00013-022-01702-8"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 RN. 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."en-US"Time-fractional Cauchy problemNonlocal nonlinearityWellposednessBesov spaces."Mild solutions to a time-fractional Cauchy problem with nonlocal nonlinearity in Besov spacesjournal-article