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Longtime behavior of semilinear multi-term fractional in time diffusion

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Abstract

In the paper, the initial-boundary value problems to a semilinear integro-differential equation with multi-term fractional Caputo derivatives are analyzed. A particular case of this equation models oxygen diffusion through capillaries. Under proper assumptions on the coefficients and a nonlinearity, the longtime behavior (as \(t\rightarrow +\infty \)) of a solution is discussed. In particular, the existence of absorbing sets in suitable functional spaces is established.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics of NAS of Ukraine, G.Batyuka st. 19, Sloviansk, 84100, Ukraine

    Nataliya Vasylyeva

  2. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy

    Nataliya Vasylyeva

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  1. Nataliya Vasylyeva
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N. Vasylyeva, as the sole author of this manuscript, carried out all the activities (research, supervision, writing, editing, etc.) associated with the writing and preparation of this article.

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Correspondence to Nataliya Vasylyeva.

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Vasylyeva, N. Longtime behavior of semilinear multi-term fractional in time diffusion. J Elliptic Parabol Equ 10, 559–593 (2024). https://doi.org/10.1007/s41808-024-00276-6

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