Stability of some porous media problems of non-integer order

Project: Research

Project Details

Description

Fractional calculus has become an appropriate platform to study complex diffusion phenomena. Of concern in this proposal are some porous media systems. As the diffusion in such media is considered to be anomalous, the existing standard laws such Ficks law and Fouriers law are not applicable. The mean square displacement does not grow linearly in this case. Fractional models constitute a suitable alternative to non-linear models which are less convenient and more costly. Therefore, we consider here fractional order porous media systems. The leading time derivatives are non-integer derivatives of order between 1 and 2. They are of Caputo type which is the commonly used derivative in applications. The problems become nonlocal problems as they take into account the whole prehistory of the states. Mathematically, this gives rise to some complications as several properties which hold in the integer case are no longer valid in the fractional case. We propose to investigate the well-posedness and stability of these problems. In particular, we will seek sufficient conditions which are able to ensure the stabilization of the problem to its rest state. The discussion will be on the different parameters involved in the problems as well as the type of damping present in the equations: weak, strong, viscoelastic and thermal.
StatusFinished
Effective start/end date1/04/211/10/22

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