Abstract We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing thermal convection, analysing these detail, and deriving critical Rayleigh wave numbers the onset convective fluid motion. In addition to linear instability theory we present careful analysis fully nonlinear stability theory. theories analysed all possess bi-Laplacian term n...

In this paper, we investigate the stabilization of a system piezoelectric beams under (Coleman or Pipkin )-Gurtin thermal law with magnetic effect. First, study Piezoelectric-Coleman-Gurtin and obtain an exponential stability result. Next, consider Piezoelectric-Gurtin-Pipkin establish polynomial energy decay rate type $t^{-1}$

due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. in this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on gurtin-murdoch continuum model to consider surface stre...

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...

Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stre...

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...