Geodesic
Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system
Electronic journal of differential equations, Tome 2016 (2016)
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.
Classification : 35D30, 35E99, 35G16, 35Q74, 35Q86
Keywords: parabolic-elliptic system, poroelasticity, thermo-poroelasticity, thermo-chemo-poroelasticity, Hadamard well-posedness 
@article{EJDE_2016__2016__a28,
     author = {Malysheva,  Tetyana and White,  Luther W.},
     title = {Sufficient conditions for {Hadamard} well-posedness of a coupled thermo-chemo-poroelastic system},
     journal = {Electronic journal of differential equations},
     year = {2016},
     volume = {2016},
     zbl = {1331.35094},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a28/}
}
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Malysheva,  Tetyana; White,  Luther W. Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system. Electronic journal of differential equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a28/