From diffusion to reaction via Gamma-convergence

Details From diffusion to reaction via Gamma-convergence From diffusion to reaction via Gamma-convergence

2009-12-30

arxiv.org/abs/0912.5077v1

Mathematics

Analysis of PDEs

18 pages, 2 figures

Scientific paper

We study the limit of high activation energy of a special Fokker-Planck equation, known as Kramers-Smoluchowski (K-S) equation. This equation governs the time evolution of the probability density of a particle performing a Brownian motion under the influence of a chemical potential H/e. We choose H having two wells corresponding to two chemical states A and B. We prove that after a suitable rescaling the solution to (K-S) converges, in the limit of high activation energy (e -> 0), to the solution of a simple system modeling the diffusion of A and B, and the reaction A <-> B. The aim of this paper is to give a rigorous proof of Kramer's formal derivation and to embed chemical reactions and diffusion processes in a common variational framework which allows to derive the former as a singular limit of the latter, thus establishing a connection between two worlds often regarded as separate. The singular limit is analysed by means of Gamma-convergence in the space of finite Borel measures endowed with the weak-* topology.

Affiliated with

Also associated with

No associations

Rating

From diffusion to reaction via Gamma-convergence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with From diffusion to reaction via Gamma-convergence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From diffusion to reaction via Gamma-convergence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-33670