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Effective Dynamics of Nonlocal Many-Particle Systems with Dynamical Constraint

Monday, December 3, 2012 - 3:15pm - 4:05pm
Keller 3-180
Michael Herrmann (Universität des Saarlandes)
In this talk we study a class of nonlocal and non-autonomous Fokker-Planck
equations that has recently been introduced
in order to describe the hysteretic behaviour of many-particle systems with dynamical control.
Relying on methods from asymptotic analysis we identify several parameter regimes
and derive reduced evolution equations for certain macroscopic quantities.
In particular, we discuss the fast reaction regime, which
can be understood by adapting Kramers formula for large deviation, and
the slow reaction regime, in which the dynamics is governed by
a subtle interplay of parabolic and hyperbolic effects.

This is joint work with Barbara Niethammer and Juan Velazquez.
MSC Code: 
34B10
Keywords: