Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system
White, Luther W.
Texas State University, Department of Mathematics
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.
Parabolic-elliptic system, Poroelasticity, Thermo-poroelasticity, Thermo-chemo-poroelasticity, Hadamard well-posedness
Malysheva, T., & White, L. W. (2016). Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system. <i>Electronic Journal of Differential Equations, 2016</i>(15), pp. 1-17.