Tetyana Malysheva, Luther W. White
Abstract:
We consider a system of fully coupled parabolic and elliptic equations
constituting the general model of chemical thermo-poroelasticity for a
fluid-saturated porous media. The main result of this paper is the
developed well-posedness theory for the corresponding initial-boundary
problem arising from petroleum rock mechanics applications.
Using the proposed pseudo-decoupling method, we establish, subject to
some natural assumptions imposed on matrices of diffusion coefficients,
the existence, uniqueness, and continuous dependence on initial and
boundary data of a weak solution to the problem. Numerical experiments
confirm the applicability of the obtained well-posedness results for
thermo-chemo-poroelastic models with real-data parameters.
Submitted February 27, 2017. Published May 24, 2017.
Math Subject Classifications: 35D30, 35E99, 35G16, 35Q74, 35Q86.
Key Words: Parabolic-elliptic system; poroelasticity; thermo-poroelasticity;
thermo-chemo-poroelasticity; existence; uniqueness; well-posedness.
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Tetyana Malysheva Department of Natural & Applied Sciences University of Wisconsin-Green Bay Green Bay, WI 54311-7001, USA email: malyshet@uwgb.edu | |
Luther W. White Department of Mathematics University of Oklahoma Norman, OK 73019-3103, USA email: lwhite@ou.edu |
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