Tetyana Malysheva, Luther W. White
This article addresses the well-posedness of a coupled parabolic-elliptic system modeling fully coupled thermal, chemical, hydraulic, and mechanical processes in porous formations that impact drilling and borehole stability. The underlying thermo-chemo-poroelastic model is a system of time-dependent parabolic equations describing thermal, solute, and fluid diffusions coupled with Navier-type elliptic equations that attempt to capture the elastic behavior of rock around a borehole. An existence and uniqueness theory for a corresponding initial-boundary value problem is an open problem in the field. We give sufficient conditions for the well-posedness in the sense of Hadamard of a weak solution to a fully coupled parabolic-elliptic initial-boundary value problem describing homogeneous and isotropic media.
Submitted December 15, 2015. Published January 8, 2016.
Math Subject Classifications: 35D30, 35E99, 35G16, 35Q74, 35Q86.
Key Words: Parabolic-elliptic system; poroelasticity; thermo-poroelasticity, thermo-chemo-poroelasticity; Hadamard well-posedness.
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| Tetyana Malysheva |
Department of Natural & Applied Sciences
University of Wisconsin-Green Bay
Green Bay, WI 54311-7001, USA
| Luther W. White |
Department of Mathematics
University of Oklahoma
Norman, OK 73019-3103, USA
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