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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). ...
Theoretical And Numerical Analysis On A ThermoElastic System With Discontinuities
 J. Comput. Appl. Math
, 1998
"... . A second order accurate numerical scheme is proposed for a thermoelastic system which models a bar made of two distinct materials. The physical parameters involved may be discontinuous across the joint of the two materials, where there might be also singular heat and/or force sources. The solutio ..."
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Cited by 4 (4 self)
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. A second order accurate numerical scheme is proposed for a thermoelastic system which models a bar made of two distinct materials. The physical parameters involved may be discontinuous across the joint of the two materials, where there might be also singular heat and/or force sources. The solution components, the temperature and the displacement, may change rapidly across the joint. By transforming the system into a different one, timemarching schemes can be used for the new system which is wellposed. The immersed interface method is employed to deal with the discontinuities of the coefficients and the singular sources. The proposed numerical method can fit both explicit and implicit formulation. For the implicit version, a stable and fast PredictionCorrection scheme is also developed. Convergence analysis shows that our method is second order accurate at all grid points in spite of the discontinuities across the interface. Numerical experiments are performed to support the theor...
FINITE ELEMENT APPROXIMATION TO A CONTACT PROBLEM IN LINEAR THERMOELASTICITY
"... Abstract. A finite element approximation to the solution of a onedimensional linear thermoelastic problem with unilateral contact of the Signorini type and heat flux is proposed. An error bound is derived and some numerical experiments are performed. 1. ..."
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Abstract. A finite element approximation to the solution of a onedimensional linear thermoelastic problem with unilateral contact of the Signorini type and heat flux is proposed. An error bound is derived and some numerical experiments are performed. 1.
DIFFUSION IN POROPLASTIC MEDIA
"... Abstract. A model is developed for the
ow of a slightly compressible
uid through a saturated inelastic porous medium. The initialboundaryvalue problem is a system that consists of the diusion equation for the
uid coupled to the momentum equation for the porous solid together with a constitutive ..."
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Abstract. A model is developed for the
ow of a slightly compressible
uid through a saturated inelastic porous medium. The initialboundaryvalue problem is a system that consists of the diusion equation for the
uid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elastoviscoplastic type. The variational form of this problem in Hilbert space is a nonlinear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible
uid, negligible porosity, or a quasistatic momentum equation. The essential sucient conditions for the wellposedness of the system consist of an ellipticity condition on the term for diusion of
uid and either
Finite difference approximations for a class of nonlocal parabolic equations
 Internat. J. Math. Math. Sci
, 1997
"... ABSTRACT. In this paper we study finite difference procedures for a class of parabolic equations with nonlocal boundary condition. The semiimplicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution ..."
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ABSTRACT. In this paper we study finite difference procedures for a class of parabolic equations with nonlocal boundary condition. The semiimplicit and fully implicit backward Euler schemes are studied. It is proved that both schemes preserve the maximum principle and monotonicity of the solution of the original equation, and fullyimplicit scheme also possesses strict monotonicity. It is also proved that finite difference solutions approach to zero as t, oo exponentially. The numerical results of some examples are presented, which support our theoretical justifications.
Wavelet based approximation in the optimal control of distributed parameter systems
, 1990
"... Wavelet based Galerkin approximation schemes for the closedloop solution of optimal linearquadratic regulator problems for distributed parameter systems are developed. The methods are based upon the finite dimensional approximation of the associated operator algebraic Riccati equation in Galerkin ..."
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Wavelet based Galerkin approximation schemes for the closedloop solution of optimal linearquadratic regulator problems for distributed parameter systems are developed. The methods are based upon the finite dimensional approximation of the associated operator algebraic Riccati equation in Galerkin subspaces spanned by families of compactly supported wavelet functions. An overview of the aspects of the theory of wavelet transforms which are useful in the development of Galerkin schemes has been provided. A brief outline of optimal linearquadratic control theory for infinite dimensional systems together with the associated approximation and convergence theories have also been included. The results of numerical studies involving two examples, control of a one dimensional heatdiffusion equation and vibration damping in a visco/thermoelastic rod, are presented and discussed. Comparisons with existing methods using both spline and modal functions are made.
Diffusion in Deforming Porous Media
"... 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 p ..."
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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 heterogeneous porous media.
Multidimensional Contact Problems in Thermoelasticity
, 1996
"... : We consider dynamical resp. quasistatic thermoelastic contact problems in R n modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical resp. quasistatic nonlinear problems and the e ..."
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: We consider dynamical resp. quasistatic thermoelastic contact problems in R n modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical resp. quasistatic nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasistatic case are also disussed. AMS subject classification: 73 B 30, 35 Q 99 Keywords and phrases: quasistatic thermoelasticity, asymptotic behavior 1 Introduction We consider dynamical resp. quasistatic thermoelastic contact problems which model the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. If\Omega ae R n (n 2) denotes the reference configuration, we assume that the smooth boundary @\Omega consists of three mutually disjoint parts \Gamma D ; \Gamma N ; \Gamma C such that @\Omega = \Gamma D [ \Gamma N [ \Gamma c ,...
MULTIDIMENSIONAL CONTACT PROBLEMS IN THERMOELASTICITY
"... Abstract. We consider dynamical and quasistatic thermoelastic contact problems in Rn modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasistatic nonlinear problems and t ..."
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Abstract. We consider dynamical and quasistatic thermoelastic contact problems in Rn modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasistatic nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing eects in the quasistatic case are also discussed. Key words. quasistatic thermoelasticity, asymptotic behavior AMS subject classications. 73B30, 35Q99
Special Issue January 2012 Numerical Solutions for Nonlocal Problem of Partial Differential Equations with Deviated Boundary Conditions
, 2012
"... Abstract: In this work, we propose a model of nonlocal partial differential equation (PDE) with deviated type function in the boundary condition. This model is solved numerically by finite difference method (FDM) using variable space grid (VSG) technique. The results obtained by this method are in a ..."
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Abstract: In this work, we propose a model of nonlocal partial differential equation (PDE) with deviated type function in the boundary condition. This model is solved numerically by finite difference method (FDM) using variable space grid (VSG) technique. The results obtained by this method are in a good agreement with the solution of the corresponding rectangular domain problem. Also, we investigated the stability analysis of problem technique by using vonNeumann method.