Direct and Inverse Problems Related to Multi-Term Fractional Diffusion Equations

Nataliya Vasylyeva (Institute of Applied Mathematics and Mechanics of NAS of Ukraine and Politecnico di Milano)

Abstract. In this talk we first discuss the initial-boundary value problems to linear and semilinear integro-differential equations with multi-term Caputo derivatives. Particular cases of these equations are the recently proposed advanced models of oxygen transport through capillaries. Under suitable conditions on the given data, the global classical and strong solvability of the associated problems is addressed. Moreover, some qualitative properties of solutions (the long-time behavior, the existence of absorbing sets) are analyzed.
The second issues discussed is the regularized reconstruction of singular parameters in the models. Namely, we proposed efficient technique to identify the order of the fractional derivative and the order of a singularity in the memory kernel for small time measurements.