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Asymptotic solutions for generalized thermoelasticity with variable thermal material properties

Wang Y., Liu D., Wang Q., Zhou J.

Archives of Mechanics

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2016

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Vol. 68, nr 3

181--202

EN

In this paper, a unified generalized thermoelastic solution with variable thermal material properties is proposed in the context of different generalized models of thermoelasticity, including thermoelasticity with one thermal relaxation time (LS theory), thermoelasticity with two thermal relaxation times (GL theory) and thermoelasticity without energy dissipation (GN theory). The unified form of governing equations is presented by introducing unifier parameters. The unified formulations are derived and given for isotropic homogenous materials with variable thermal material properties. The Laplace transform techniques and the Kirchhoff’s transformation are used to obtain general solutions for any set of boundary conditions in the physical domain. Asymptotic solutions for a specific problem of an elastic half-space with variable thermal conductivity and a specific heat, whose boundary is subjected to a thermal shock, are derived by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, some generalized thermoelastic phenomena are observed. Especially, the jumps at the wavefronts induced by the propagation of finite signal speed for the heat are clearly noticed. In addition, the effect of variable characteristics of material properties on thermoelastic behaviors is revealed by a comparison with the results obtained in the case of constant material properties.

2

Asymptotic solution for rotating disk flow in a porous medium

Attia H. A.

Mechanics and Mechanical Engineering

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2010

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Vol. 14, nr 1

119-136

EN

In this paper, we present asymptotic solution to a Navier-Stokes equation of von Karman type for the flow due to a rotating disk in a porous medium. Asymptotic solutions to a Navier-Stokes equation is given in the case of small as well as large values of the porosity parameter β whose coefficients are obtained in closed form in terms of properly scaled von Karman's similarity coordinate. Straining of coordinates is used to remove secular terms and enable to obtain expressions that can be used to determine the coefficients of the expansions to any order. A comparison of the asymptotic solution with an exact numerical solution for the governing nonlinear differential equations is presented.

3

Invariant measures for stochastic heat equations

Tessitore G., Zabczyk J.

Probability and Mathematical Statistics

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1998

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Vol. 18, Fasc. 2

271--287

EN

The paper is concerned with the asymptotic behaviour of solutions to the nonlinear stochastic heat equations, with spatially homogeneous noise, in the whole space. Sufficient conditions for the existence of invariant measures, in weighted spaces of locally square-integrable functions, are given. For linear equations with multiplicative noise an invariant measure, supported by positive functions, is constructed. The existence of a stationary solution to the vector Burgers equations is obtained as an application of the general theory.