Electron. J. Differential Equations, Vol. 2017 (2017), No. 137, pp. 1-22.

Well-Posedness of a fully coupled thermo-chemo-poroelastic system with applications to petroleum rock mechanics

Tetyana Malysheva, Luther W. White

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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