Existence of weak solutions is proved for the unsteady Darcy-Brinkman problem coupled to miscible reactive flows, with global existence when initial concentration is between 0 and 1, finite-time blow-up when above 1, uniqueness in 2D, and finite-element simulations confirming the behavior.
De Wit, Chemo-hydrodynamic patterns in porous media, Philosophical Transactions of the Royal Society A: Mathe- matical, Physical and Engineering Sciences374, 20150419 (2016)
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Existence and uniqueness of solutions of unsteady Darcy-Brinkman problem for modelling miscible reactive flows in porous media
Existence of weak solutions is proved for the unsteady Darcy-Brinkman problem coupled to miscible reactive flows, with global existence when initial concentration is between 0 and 1, finite-time blow-up when above 1, uniqueness in 2D, and finite-element simulations confirming the behavior.