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This paper considers a unit cube made of a compressible, transversely isotropic elastic material, with the direction of transverse isotropy being aligned normal to one pair of the cube's faces, and investigates the stability of a dilatation equilibrium state of that cube, with respect to...
Using the method of integral (invariant) manifolds, the intrinsic low-dimensional manifolds (ILDM) method is analysed. This is a method for identifying invariant manifolds of a system's slow dynamics and has proven to be an efficient tool in modelling of laminar and turbulent combustion. It...
In this paper, a new theory of generalized thermoelasticity has been constructed by taking into account the theory of heat conduction in deformable bodies, which depends on two distinct temperatures, the conductive temperature and the thermodynamic temperature, where the difference between these...
We present a discussion of the exponential decay—in particular, giving explicit sharp decay rates—for solutions to the system of classical thermoelasticity as well as for that of thermoelasticity with second sound. The relevance of the latter model in contrast to the first one with respect to...
It is demonstrated here that there exist initial layers to singularly perturbed Volterra equations whose thicknesses are not of the order of magnitude of O( ϵ ), ϵ → 0. It is also shown that the initial-layer theory is extremely useful because it allows one to construct the approximate...
This paper considers the propagation of a plane thermoelastic wave in an infinite homogeneous isotropic plate subjected to either isothermal or thermally insulated traction-free boundary conditions. The primary concerns are the derivation and numerical examination of the dispersion relations...
We present an explicit expression for the surface-impedance tensor associated with a compressible monoclinic elastic material in a state of plane strain. Among a wide range of applications, such an explicit expression can, for instance, be used to write down an explicit secular equation for the...
We consider generalization of the theory for the evolution of reaction–diffusion and accelerating wavefronts in KPP-type systems as developed in Needham (2004, Proc. R. Soc. Lond. A , 460 , 1921–1934) (DN). These generalizations allow for the removal of a number of technical restrictions...
This work is devoted to the classical Lie symmetry analysis of a class of systems of two quasilinear multidimensional reaction–diffusion (RD) equations having variable diffusivities. Moreover, conservation laws for RD systems containing such diffusivities are constructed. Some generalizations...
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