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Unsaturated deformable porous media flow with thermal phase transition
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SYSNO ASEP 0481815 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Unsaturated deformable porous media flow with thermal phase transition Author(s) Krejčí, Pavel (MU-W) RID, SAI, ORCID
Rocca, E. (IT)
Sprekels, J. (DE)Source Title Mathematical Models and Methods in Applied Sciences. - : World Scientific Publishing - ISSN 0218-2025
Roč. 27, č. 14 (2017), s. 2675-2710Number of pages 36 s. Language eng - English Country SG - Singapore Keywords porous media ; phase transitions ; existence of solutions Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects GA15-12227S GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000418031700003 EID SCOPUS 85034024080 DOI 10.1142/S0218202517500555 Annotation In this paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquid–solid phase transformations in groundwater flows. The system of equations is derived here from the conservation principles for mass, momentum, and energy and from the Clausius–Duhem inequality for entropy. It couples the evolution of the displacement in the matrix material, of the capillary pressure, of the absolute temperature, and of the phase fraction. Mathematical results are proved under the additional hypothesis that inertia effects and shear stresses can be neglected. For the resulting highly nonlinear system of two PDEs, one ODE and one ordinary differential inclusion with natural initial and boundary conditions, existence of global in time solutions are proved by means of cut-off techniques and suitable Moser-type estimates. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2018
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