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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). ...
A Stefan problem modelling crystal dissolution and precipitation
, 2006
"... A simple 1D model for crystal dissolution and precipitation is presented. The model equations resemble a onephase Stefan problem and involve nonlinear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fix ..."
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Cited by 8 (1 self)
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A simple 1D model for crystal dissolution and precipitation is presented. The model equations resemble a onephase Stefan problem and involve nonlinear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fixed domain and applying a regularization, we prove the existence and uniqueness of a solution. The paper is concluded by numerical simulations.
A NONLOCAL PARABOLIC SYSTEM In LINEAR THERMOELASTICITY
 in Dynamics of Continuous, Discrete and Impulsive Systems
, 1996
"... A system of parabolic integrodifferential equations arising in the study of thermoelastic contact of two rods is considered. The questions of existence, uniqueness and continuous dependence of the solution upon the data are demonstrated via the theoretical potential solution representation techniqu ..."
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A system of parabolic integrodifferential equations arising in the study of thermoelastic contact of two rods is considered. The questions of existence, uniqueness and continuous dependence of the solution upon the data are demonstrated via the theoretical potential solution representation technique and theory of Volterra equations of second kind. An application to linear thermoelasticity is also given. Keywords: Parabolic, integrodifferential, nonlocal, thermoelastic contact. AMS(MOS) subject classification:35K50, 73C25, 73J05. 1. Introduction In this paper we consider the following parabolic system of finding U = (u 1 (x; t); u 2 (x; t)) such that u 1 t \Gamma c 1 u 1 xx = b 1 l 1 d dt maxfI(U); 0g ; in Q 1 T = (0; l 1 ) \Theta J; (1.1) u 2 t \Gamma c 2 u 2 xx = b 2 1 \Gamma l 2 d dt maxfI(U); 0g ; in Q 2 T = (l 2 ; 1) \Theta J; (1.2) u 1 (x; 0) = OE 1 (x); 0 ! x ! l 1 ; (1.3) u 2 (x; 0) = OE 2 (x); l 2 ! x ! 1; (1.4) Â¯ 1 u 1 x (0; t) + 1 u 1...
A STEFAN PROBLEM MODELLING DISSOLUTION AND PRECIPITATION IN POROUS MEDIA
"... Abstract. A simple onedimensional model for crystal dissolution and precipitation is presented. The model equations resemble a onephase Stefan problem and involve nonlinear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transfor ..."
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Abstract. A simple onedimensional model for crystal dissolution and precipitation is presented. The model equations resemble a onephase Stefan problem and involve nonlinear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fixed domain and applying a regularization, we prove the existence and uniqueness of a solution. The paper is concluded by numerical simulations. 1. Introduction. This
A Nonlocal Parabolic System modelling Axially Symmetric Thermoelastic Contact of Two Discs
, 1996
"... A system of parabolic integrodifferential equations modelling homogeneous and isotropic elastic thin discs subject to axially symmetric temperature fields and displacements is studied. Under some appropriate assumptions the questions of existence, uniqueness and continuous dependence of the solutio ..."
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A system of parabolic integrodifferential equations modelling homogeneous and isotropic elastic thin discs subject to axially symmetric temperature fields and displacements is studied. Under some appropriate assumptions the questions of existence, uniqueness and continuous dependence of the solutions upon the data is demonstrated. The main feature of our method in this paper is that the difficulties associated with this physical problem can been seen clearly and overcome easily via the decoupling procedures and transformations. 1. Introduction. We consider two dissimilar homogeneous and isotropic thin discs subject to axially symmetric temperature fields ` i and displacements u i (i = 1; 2). In addition it is assumed that the thermoelastic stresses oe i (i = 1; 2) of the bodies are also axially symmetric, thus ` i ; u i and oe i (i = 1; 2) are functions of the radius r and time t, relative to the reference configuration of elastic disc 0 ! r ! r 1 and annual disc r 2 ! r ...
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"... Abstract. We report on some recent progress in the mathematical theory of nonlinear fluid transport and poromechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the coupled pressure and stress distributions within a deforming heteroge ..."
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Abstract. We report on some recent progress in the mathematical theory of nonlinear fluid transport and poromechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the coupled pressure and stress distributions within a deforming heterogeneous porous structure. The goal of this work is to develop a set of mathematical models of coupled flow and deformation processes as a basis for fundamental research on the theoretical and numerical modeling and simulation of flow in deforming