In this talk we propose a numerical scheme to investigate the stability of steady states of the nonlinear Gurtin–MacCamy system which is a basic model in population dynamics. In fact the analysis of stability is usually performed by the study of transcendental characteristic equations that are too difficult to approach by analytical methods. The method is based on the discretization of the infi...

The numerical approximation scheme for solving the nonlinear initial value problem ∂tb(v) = ∂xxβ(x, v) + β(x, v) with periodic boundary conditions is presented. Local existence and uniqueness of a solution and convergence of approximations is a consequence of the results of Mikula and Kačur (1996), where the anisotropic curvature driven evolution of plane convex curves is studied. The considere...

In this paper we discuss some thermoelastic and thermoviscoelastic models obtained from the Gurtin theory, based on invariance of entropy under time reversal. We derive differential systems where temperature velocity are ruled by generalized versions Moore-Gibson-Thompson equation. one-dimensional case, provide a complete analysis evolution, establishing an existence uniqueness result valid for...

TIME-REVERSAL AND SYMMETRY IN THE THERMODYNAMICS OF MATERIALS WITH MEMORY by Morton E. Gurtin We here study, within the framework of the thermodynamics of materials with memory, the notion of invariance under timereversal. In particular, we establish conditions that are both necessary and sufficient for the infinitesmal entropy production to display such invariance.

Dolphin Research Australia Inc., Byron Bay, NSW, Australia, Marine Ecology Research Centre, Southern Cross University, Lismore, NSW, Australia, Department of Biological Sciences, Macquarie University, North Ryde, NSW, Australia, Cetacean Research Unit, School of Veterinary and Life Sciences, Murdoch University, Murdoch, WA, Australia, 5 StatPlan Consulting Pty Ltd, Woodburn, NSW, Australia, 6 A...

In this paper we consider a linear thermoelastic system of Timoshenko type where the heat conduction is given by linearized law Gurtin-Pipkin. An existence and uniqueness result proved use semigroup approach. We establish an exponential stability without any assumption on wave speeds once here have fully damped system.