Technion - Israel Institute of Technology
Department of Mathematics
DATE: Tuesday, March 22, 2011
SPEAKER: Nitsan Ben-Gal (Weizmann)
TITLE:  Attraction at Infinity: Constructing Non-Compact Global
        Attractors in the Slowly Non-Dissipative Realm
PLACE: Room 814, Amado Mathematics Building, Technion
TIME: 14:30
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 solutions
to the equation in question. Nevertheless, the classic global attractor
for such systems is defined to be compact, and thus attractor theory 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 the classical global attractor, 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 for 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..
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