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Mathematics Colloquium: Non-Compact Global Attractors

Friday, 01 November, 2013

SPEAKER:  Prof. Nitsan Ben-Gal, IMA-University of Minnesota

TITLE:  Non-Compact Global Attractors and Infinite-Time Blow-Up

ABSTRACT: Global attractors and their deconstructions provide us with a versatile tool for studying the long-time behavior of solutions to reaction-diffusion equations.  The majority of global attractor theory assumes that the equation in question is dissipative, but recent work has shown that similar results can be obtained for non-dissipative reaction-diffusion equations exhibiting infinite-time blow-up of solutions without any finite-time blow-up.  Such phenomena appear in the analysis of various models ranging from suspension bridges to Rayleigh-Bénard convection to tumor growth.  In this talk I will discuss my recent results in this area, as well as some of the geometric methods which yield them, including bifurcation diagrams, Fučik spectra, and nodal properties.  This is joint work with Kristen Moore and Juliette Hell.

Refreshments available at 3:10 p.m.




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