Applied Analysis Reading Group

21 May 2015: Upanshu Sharma (Eindhoven)

Variational approach to the overdamped limit of the Kramers equations

Coarse-graining or dimension reduction is the procedure of approximating a system by a simpler or lower dimensional one. This is typically achieved by passage to the limit of some parameter in the original system. Variational-evolution structures have been successfully used in recent years to pass to the limit in case of dissipative (gradient-flow) systems. However these structures do not straightforwardly apply to systems which additionally have inertial effects. In this talk, I will present a variational technique arising from large-deviations theory which applies to a class of systems where both dissipative and inertial effects are present. I will present the technique by means of an example, deriving the overdamped or high-friction limit of the Kramers equation. This is joint work with M. Hong Duong, Agnes Lamacz and Mark A. Peletier.

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