Discontinuity waves in temperature and diffusion models

We analyse shock wave behaviour in a hyperbolic diffusion system with a general forcing term which is qualitatively not dissimilar to a logistic growth term. The amplitude behaviour is interesting and depends critically on a parameter in the forcing term. We also develop a fully nonlinear acceleration wave analysis for a hyperbolic theory of diffusion coupled to temperature evolution. We consider a rigid body and we show that for three-dimensional waves there is a fast wave and a slow wave. The amplitude equation is derived exactly for a one-dimensional (plane) wave and the amplitude is found for a wave moving into a region of constant temperature and solute concentration. This analysis is generalized to allow for forcing terms of Selkov–Schnakenberg, or Al Ghoul-Eu cubic reaction type. We briefly consider a nonlinear acceleration wave in a heat conduction theory with two solutes present, resulting in a model with equations for temperature and each of two solute concentrations. Here it is shown that three waves may propagate

Christov-Morro theory for non-isothermal diffusion

We propose a theory for diffusion of a substance in a body allowing for changes in temperature. The key aspect is that the body is allowed to deform although we restrict our attention to the case where the velocity field is known. In accordance with recent developments in the literature, we concentrate on a situation where diffusion and temperature diffusion are governed by equations which have more of a hyperbolic nature than parabolic. Since this involves relaxation time equations for both the heat flux and the solute flux the fact that the body can deform necessitates the use of appropriate objective time derivatives. In this regard our work is based on recent work of Christov and Morro on heat transport in a moving body. An analysis of well posedness of the theory is commenced in that we establish the uniqueness of a solution to the boundary-initial value problem, and continuous dependence on the initial data for the same. (C) 2011 Elsevier Ltd. All rights reserved

Spatial behaviour of solutions in the plane Stokes flow

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On the bending of microstretch elastic plates

This paper is concerned with the linear theory of microstretch elastic solids introduced by Eringen (A.C. Eringen, in: Prof. Dr. Mustafa Inan Anisina, Ari Kitabevi Matbaasi, Istanbul, 1971, pp. 1-18; A.C. Eringen, Int. J. Eng. Sci. 28 (1990) 1290-1301). First, a theory of bending of homogeneous and isotropic plates is studied. Then, a uniqueness theorem, with no definiteness assumptions on the elastic coefficients, is presented. (C) 1999 Elsevier Science Ltd. All rights reserved