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dc.contributor.authorBrun, Mats Kirkesæther
dc.contributor.authorRadu, Florin Adrian
dc.contributor.authorAhmed, Elyes
dc.contributor.authorNordbotten, Jan Martin
dc.PublishedBrun MK, Radu FA, Ahmed E, Nordbotten JM. Well-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transport. Journal of Mathematical Analysis and Applications. 2019;471(1-2):239-266eng
dc.description.abstractThis paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists of a momentum balance equation, a mass balance equation, and an energy balance equation, fully coupled and nonlinear due to a convective transport term in the energy balance equation. The aim of this article is to investigate, in the context of mixed formulations, the existence and uniqueness of a weak solution to this model problem. The primary variables in these formulations are the fluid pressure, temperature and elastic displacement as well as the Darcy flux, heat flux and total stress. The well-posedness of a linearized formulation is addressed first through the use of a Galerkin method and suitable a priori estimates. This is used next to study the well-posedness of an iterative solution procedure for the full nonlinear problem. A convergence proof for this algorithm is then inferred by a contraction of successive difference functions of the iterates using suitable norms.en_US
dc.relation.ispartof<a href="" target="blank">Upscaling, analysis, and iterative numerical solution schemes for thermo-poroelasticity</a>en_US
dc.rightsAttribution CC BYeng
dc.subjectNonlinear convective transporteng
dc.subjectBiot's modeleng
dc.subjectGalerkin's methodeng
dc.subjectConvergence analysiseng
dc.titleWell-posedness of the fully coupled quasi-static thermo-poroelastic equations with nonlinear convective transporten_US
dc.typePeer reviewed
dc.typeJournal article
dc.rights.holderCopyright 2018 The Author(s)en_US
dc.source.journalJournal of Mathematical Analysis and Applications

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