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This paper is concerned with the analysis of the quasi-staticthermo-poroelastic model. This model is nonlinear and includes thermal effectscompared to the classical quasi-static poroelastic model (also known as Biot'smodel). It consists of a momentum balance equation, a mass balance equation,and an energy balance equation, fully coupled and nonlinear due to a convectivetransport term in the energy balance equation. The aim of this article is toinvestigate, in the context of mixed formulations, the existence and uniquenessof a weak solution to this model problem. The primary variables in theseformulations are the fluid pressure, temperature and elastic displacement aswell as the Darcy flux, heat flux and total stress. The well-posedness of alinearized formulation is addressed first through the use of a Galerkin methodand suitable a priori estimates. This is used next to study the well-posednessof an iterative solution procedure for the full nonlinear problem. Aconvergence proof for this algorithm is then inferred by a contraction ofsuccessive difference functions of the iterates using suitable norms.

Well-posedness of the fully coupled quasi-static thermo-poro-elastic equations with nonlinear convective transport