Fundamental solution of kinetic fokker-planck operator with anisotropic nonlocal dissipativity

Xicheng Zhang

doi:10.1137/130926493

Fundamental solution of kinetic fokker-planck operator with anisotropic nonlocal dissipativity

Xicheng Zhang^*

^*Corresponding author for this work

Wuhan University

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic Lévy process, and the drift term is allowed to be cubic growth.

Original language	English
Pages (from-to)	2254-2280
Number of pages	27
Journal	SIAM Journal on Mathematical Analysis
Volume	46
Issue number	3
DOIs	https://doi.org/10.1137/130926493
Publication status	Published - 2014
Externally published	Yes

Keywords

Anisotropic lévy process
Kinetic fokker-planck operator
Malliavin calculus

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10.1137/130926493

Cite this

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title = "Fundamental solution of kinetic fokker-planck operator with anisotropic nonlocal dissipativity",

abstract = "By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic L{\'e}vy process, and the drift term is allowed to be cubic growth.",

keywords = "Anisotropic l{\'e}vy process, Kinetic fokker-planck operator, Malliavin calculus",

author = "Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright}2014 Society for Industrial and Applied Mathematics.",

year = "2014",

doi = "10.1137/130926493",

language = "English",

volume = "46",

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T1 - Fundamental solution of kinetic fokker-planck operator with anisotropic nonlocal dissipativity

AU - Zhang, Xicheng

PY - 2014

Y1 - 2014

N2 - By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic Lévy process, and the drift term is allowed to be cubic growth.

AB - By using the probability approach (the Malliavin calculus), we prove the existence of smooth fundamental solutions for degenerate kinetic Fokker-Planck equation with anisotropic nonlocal dissipativity, where the dissipative term is the generator of an anisotropic Lévy process, and the drift term is allowed to be cubic growth.

KW - Anisotropic lévy process

KW - Kinetic fokker-planck operator

KW - Malliavin calculus

UR - https://www.scopus.com/pages/publications/84987597489

U2 - 10.1137/130926493

DO - 10.1137/130926493

M3 - Article

AN - SCOPUS:84987597489

SN - 0036-1410

VL - 46

SP - 2254

EP - 2280

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

Fundamental solution of kinetic fokker-planck operator with anisotropic nonlocal dissipativity

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Keywords

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