Longtime behavior of semilinear multi-term fractional in time diffusion
Journal of Elliptic and Parabolic Equations(2024)
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→ +∞ ) of a solution is discussed. In particular, the existence of absorbing sets in suitable functional spaces is established.
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Key words
Semilinear multi-term subdiffusion,Caputo derivative,Longtime behavior,Absorbing sets,Primary 35R11,35B45,Secondary 35B65,26A33,35Q92
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