A priori estimates to solutions of the time-fractional convection–diffusion–reaction equation coupled with the Darcy system
Hendy A.S. Zaky M.A.
June 2022Elsevier B.V.
Communications in Nonlinear Science and Numerical Simulation
2022#109
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.
A priori estimates , Darcys law , Existence and uniqueness , Time fractional convection–diffusion
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Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg, 620002, Russian Federation
Department of Applied Mathematics, National Research Centre, Cairo, Dokki, 12622, Egypt
Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Computational Mathematics and Computer Science
Department of Applied Mathematics
Department of Mathematics
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