The First Boundary-Value Problem for the Fokker–Planck Equation with One Spatial Variable

The Fokker–Planck equation with one spatial variable without the lowest term is considered. The diffusion coefficient is assumed to be measurable, bounded, and separated from zero. The existence of a weak fundamental solution of the Fokker–Planck equation is proved and some properties of this soluti...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 283; no. 3; pp. 397 - 401
Main Author Konenkov, A. N.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.08.2024
Springer
Springer Nature B.V
Subjects
Boundary value problems
Continuity (mathematics)
Diffusion coefficient
Fokker-Planck equation
Mathematical analysis
Mathematics
Mathematics and Statistics
35A08
first boundary-value problem
Fokker–Planck equation
fundamental solution
35D30
parabolic equation
35K10
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Summary:The Fokker–Planck equation with one spatial variable without the lowest term is considered. The diffusion coefficient is assumed to be measurable, bounded, and separated from zero. The existence of a weak fundamental solution of the Fokker–Planck equation is proved and some properties of this solution are established. Under the additional assumption that the leading coefficient is a Hölder function, we consider the first boundary-value problem in a semi-bounded domain. We assume that the right-hand side of the equation and the initial function are zero and the boundary function is continuous. We prove the solvability of this problem in the class of bounded functions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07267-x