Longtime behavior of semilinear multi-term fractional in time diffusion

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 $t\to +\infty$) of a solution is discussed. In particular, the existence of absorbing sets in suitable functional spaces is established.