Picture of person typing on laptop with programming code visible on the laptop screen

World class computing and information science research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.

Explore

Memory driven instability in a diffusion process

Duffy, B.R. and Grinfeld, M. and Freitas, P. (2002) Memory driven instability in a diffusion process. SIAM Journal on Mathematical Analysis, 33 (5). pp. 1090-1106. ISSN 0036-1410

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

We consider the ndimensional version of a model proposed by Olmstead et al. [SIAM J. Appl. Math., 46 (1986), pp. 171--188] for the flow of a non-Newtonian fluid in the presence of memory. We prove the existence of a global attractor and obtain conditions for the existence of a Lyapunov functional, which allows us to give a full description of this attractor in a certain region of the parameter space in the bistable case. We then study the stability and bifurcation of stationary solutions and, in particular, prove that for certain values of the parameters it is not possible to stabilize the flow by increasing a Rayleigh-type number. The existence of periodic and homoclinic orbits is also shown by studying the Bogdanov--Takens singularity obtained from a center manifold reduction.