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Diffusion in PoroElastic Media
 Jour. Math. Anal. Appl
, 1998
"... . Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of se ..."
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. Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasistatic system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasistatic assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...
Discrete Models Of Coupled Dynamic Thermoelasticity For StressTemperature Formulations
 Comp., University of Southern Queensland
"... In this article, the author studies the properties of discrete approximations for mathematical models of coupled thermoelasticity in the stresstemperature formulation. Since many applied problems deal with steep gradients of thermal fields, the main emphasis is given to the investigation of nonsmo ..."
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Cited by 1 (1 self)
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In this article, the author studies the properties of discrete approximations for mathematical models of coupled thermoelasticity in the stresstemperature formulation. Since many applied problems deal with steep gradients of thermal fields, the main emphasis is given to the investigation of nonsmooth solutions of nonstationary thermoelasticity. Convergence of operatordifference schemes on weak solutions of thermoelasticity is proved, and the dispersion analysis of models is performed. Error estimates and the results of computational experiments are presented. Key words: hyperbolicparabolic models, operatordifference schemes for thermoelasticity problems, weak solutions, optimal error control. 1 Mixed Modes in Dynamics Described by Mathematical Models of Coupled Field Theory. In essence, any mathematical model describes a transformation of different types of energy. The recognition of this fact leads to an integral reformulation of differential models. On the one hand, such a r...