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Open Access research with a European policy impact...

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 Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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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

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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.