A priori estimates to solutions of the time-fractional convection-diffusion-reaction equation coupled with the Darcy system

摘要

We consider the Darcy flow equation coupled with the Caputo time-fractional convection-reaction-diffusion equations. This system describes the concentration distribution of a fluid running through a porous medium. A priori estimates are established for the solution by employing the method of energy inequalities. The existence, uniqueness and regularity properties of a weak solution are studied. Our analysis relies on two novel and different methodologies in combination with two alternative variational formulations. (C) 2022 Elsevier B.V. All rights reserved.