DC Field | Value | Language |
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dc.contributor.author | Hwang, Hyung Ju | - |
dc.contributor.author | Jang, Juhi | - |
dc.contributor.author | Velazquez, Juan J. L. | - |
dc.date.accessioned | 2019-12-03T11:50:25Z | - |
dc.date.available | 2019-12-03T11:50:25Z | - |
dc.date.created | 2019-02-13 | - |
dc.date.issued | 2019-03 | - |
dc.identifier.issn | 0003-9527 | - |
dc.identifier.uri | https://oasis.postech.ac.kr/handle/2014.oak/100180 | - |
dc.description.abstract | We describe the structure of solutions of the kinetic Fokker-Planck equations in domains with boundaries near the singular set in one-space dimension. We study in particular the behaviour of the solutions of this equation for inelastic boundary conditions which are characterized by means of a coefficient r describing the amount of energy lost in the collisions of the particles with the boundaries of the domain. A peculiar feature of this problem is the onset of a critical exponent r(c) which follows from the analysis of McKean (J Math Kyoto Univ 2:227-235 1963) of the properties of the stochastic process associated to the Fokker-Planck equation under consideration. In this paper, we prove rigorously that the solutions of the considered problem are nonunique if r <r(c) and unique if rc<r1. In particular, this nonuniqueness explains the different behaviours found in the physics literature for numerical simulations of the stochastic differential equation associated to the Fokker-Planck equation. In the proof of the results of this paper we use several asymptotic formulas and computations in the companion paper (Hwang in Q Appl Math 2018). | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.relation.isPartOf | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | - |
dc.title | Nonuniqueness for the Kinetic Fokker-Planck Equation with Inelastic Boundary Conditions | - |
dc.type | Article | - |
dc.identifier.doi | 10.1007/s00205-018-1299-0 | - |
dc.type.rims | ART | - |
dc.identifier.bibliographicCitation | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, v.231, no.3, pp.1309 - 1400 | - |
dc.identifier.wosid | 000456309400001 | - |
dc.citation.endPage | 1400 | - |
dc.citation.number | 3 | - |
dc.citation.startPage | 1309 | - |
dc.citation.title | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | - |
dc.citation.volume | 231 | - |
dc.contributor.affiliatedAuthor | Hwang, Hyung Ju | - |
dc.identifier.scopusid | 2-s2.0-85052648331 | - |
dc.description.journalClass | 1 | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | N | - |
dc.type.docType | Article | - |
dc.subject.keywordPlus | VLASOV-POISSON SYSTEM | - |
dc.subject.keywordPlus | REGULARITY | - |
dc.subject.keywordPlus | OPERATORS | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mechanics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalResearchArea | Mechanics | - |
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