Electron. J. Differential Equations, Vol. 2020 (2020), No. 63, pp. 1-26.

Global weak solutions to degenerate coupled transport processes in partially saturated deformable elastic-inelastic porous media

Michal Benes

In this work we prove the existence of global weak solutions to a degenerate and strongly coupled parabolic system arising from the transport processes through partially saturated deformable porous materials. The hygro-thermal model is coupled with quasi-static evolution equations modeling elastic and inelastic mechanical deformations. Physically relevant Newton boundary conditions are considered for water pressure and temperature of the porous system. The traction boundary condition is imposed on the deformable solid skeleton of the porous material. Degeneration occurs in both elliptic and parabolic part of the balance equation for mass of water. The coupling between water pressure, temperature, stress tensor and internal variables occurs in transport coefficients, constitutive functions and the decomposition of the total strain tensor into elastic and plastic parts due to mechanical effect and strain tensor due to thermal expansion.

Submitted October 8, 2019. Published June 19, 2020.
Math Subject Classifications: 35A01, 35D30, 35B65, 35B45, 35B50, 35K15, 35K40.
Key Words: Second-order parabolic systems, global solution; porous media; smoothness and regularity; coupled transport processes; elastic-inelastic solids; internal variables; traction problem; constitutive equations; coercivity; convexity.

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Michal Benes
Department of Mathematics
Faculty of Civil Engineering
Czech Technical University in Prague
Th\'akurova 7, 166 29 Prague 6, Czech Republic
email: michal.benes@cvut.cz

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