On the Langevin equation with variable friction

We study two asymptotic problems for the Langevin equation with variable friction coefficient. The first is the small mass asymptotic behavior, known as the Smoluchowski–Kramers approximation, of the Langevin equation with strictly positive variable friction. The second result is about the limiting...

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Published inCalculus of variations and partial differential equations Vol. 56; no. 6; pp. 1 - 26
Main Authors Ishii, Hitoshi, Souganidis, Panagiotis E., Tran, Hung V.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects
Analysis
Asymptotic properties
Calculus of Variations and Optimal Control; Optimization
Coefficient of friction
Control
Friction
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
35B25
49L25
35B40
Online AccessGet full text
ISSN0944-2669
1432-0835
DOI10.1007/s00526-017-1240-7

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Summary:We study two asymptotic problems for the Langevin equation with variable friction coefficient. The first is the small mass asymptotic behavior, known as the Smoluchowski–Kramers approximation, of the Langevin equation with strictly positive variable friction. The second result is about the limiting behavior of the solution when the friction vanishes in regions of the domain. Previous works on this subject considered one dimensional settings with the conclusions based on explicit computations.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-017-1240-7