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
Michal Benes
Abstract:
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.
DOI: 10.58997/ejde.2020.63
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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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