1 Australian Centre for Necrotrophic Fungal Pathogens, SABC, Faculty of Health Sciences, 11 Murdoch University, Murdoch 6150, Australia. 2 Australian Research Council Centre of 12 Excellence in Plant Energy Biology, The University of Western Australia, Crawley 6009, 13 Australia. 4 School of Biological Sciences and Biotechnology, Division of Science and 14 Engineering, Murdoch University, Murdo...

We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location i...

In this article, we study the stability of a porous thermoelastic system with Gurtin-Pipkin flux. Under suitable assumptions for derivative heat flux relaxation kernel, establish existence and uniqueness solution by applying semigroup theory, prove exponential without considering wave velocity means estimates resolvent

where V and k are, respectively, the normal velocity and curvature of the interface. Equation (1) is sometimes called the “curve shortening problem” because it is the negative L2-gradient flow of the length of the interface. By drawing pictures, one can be easily convinced that a simple closed curve stays simple and smooth along (1) and shrinks to a point in finite time, with the limiting shape...

Treena I. Burgess, Centre for Phytophthora Science and Management, School of Biological Sciences and Biotechnology, Murdoch University, Murdoch, WA 6150, Australia; Janet L. Webster and Juanita A. Ciampini, Department of Environment and Conservation, Science Division, Locked Bag 104, Bentley D.C., WA 6983, Australia; Diane White and Giles E. StJ. Hardy, Centre for Phytophthora Science and Manag...

1 Department of Physics and Astronomy, The University of Nebraska, Lincoln, NE 68588-0111, USA 2 Department of Physics, Voronezh State University, Voronezh 394006, Russia 3 Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia 4 Centre for Atomic, Molecular and Surface Physics, School of Mathematical and Physical Sciences, Murdoch Un...

Three direct integration schemes for the matrix equations of motion of structural dynamics-the Newmark generalized acceleration operator, the Wilson averaging variant of the linear acceleration operator and an averaging method based on a variational principle derived by Gurtin-are investigated for stability and approximation viscosity. Using established techniques developed by J. von Neumann an...

In this paper, we study the long-time dynamics of a nonlinear model piezoelectric beam subjected to magnetic and thermal effects. The effect acts on system according Coleman-Gurtin law. Using semigroup theory, prove existence uniqueness solutions. global attractors is proved by showing that dynamical associated with solutions quasi-stable gradient. To conclude, show family continuous dense resi...