PDE seminar Non-compact global attractors and dynamics at infinity for slowly non-dissipative reaction-diffusion equations

2011-2-8 16:30 - 2011-2-8 17:30
Faculty of Science Building #3 Room 202
Nitsan Ben-Gal (Weizmann Institute of Science, Israel)
One of the primary tools for understanding the much-studied realm of
reaction-diffusion equations is the global attractor, which provides
us with a qualitative understanding of the governing behaviors of the
equation in question. Nevertheless, the classic global attractor
for such systems is defined to be compact, and thus has previously
excluded such analysis from being applied to non-dissipative
reaction-diffusion equations.

In this talk I will present recent results in which I developed a
non-compact analogue to this classical concept, and will discuss the
methods derived in order to obtain a full decomposition of the
non-compact global attractor for a slowly non-dissipative
reaction-diffusion equation. In particular, attention will be paid to
the nodal property techniques and reduction methods which form a
critical underpinning of asymptotics research in both dissipative and
non-dissipative evolutionary equations. I will discuss the
concepts of the ‘completed inertial manifold’ and ‘non-compact
global attractor’, and show how these in particular allow us to
produce equivalent results for a class of slowly non-dissipative
equations as have been achieved for dissipative equations.
Additionally, I will address the behavior of solutions to
slowly non-dissipative equations approaching and at infinity, the
realm which presents both the challenges and rewards of removing the
necessity of dissipativity.

* Please note change in date this week.