Asymptotics for scaled Kramers–Smoluchowski equations in several dimensions with general potentials

  • Insuk Seo
  • Peyam TabrizianEmail author


In this paper, we generalize the results of Evans and Tabrizian (SIAM J Math Anal 48:2944–2961, 2016), by deriving asymptotics for the time-rescaled Kramers–Smoluchowski equations, in the case of a general non-symmetric potential function with multiple wells. The asymptotic limit is described by a system of reaction–diffusion equations whose coefficients are determined by the Kramers constants at the saddle points of the potential function and the Hessians of the potential function at global minima.

Mathematics Subject Classification

35K15 35K57 35J20 



The authors wish to thank Professor Lawrence C. Evans for his fruitful discussions. The research of I. Seo is supported by the National Research Foundation of Korea NRF grant funded by the Korean government MSIT (Project 2018R1C1B6006896).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical Sciences and Research Institute of MathematicsSeoul National UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsUniversity of California, IrvineIrvineUSA

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