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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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Cited by 10 (7 self)
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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). ...
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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Cited by 2 (0 self)
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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.
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 2 (2 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.
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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Cited by 1 (0 self)
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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.
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 ,...
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.
Electronic Journal of Qualitative Theory of Differential Equations
"... Multiple solutions of nonlocal boundary value problems for fractional differential equations on the halfline ∗ ..."
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Multiple solutions of nonlocal boundary value problems for fractional differential equations on the halfline ∗