Heat kernel estimates for time fractional equations

Zhen Qing Chen; Panki Kim; Takashi Kumagai; Jian Wang

doi:10.1515/forum-2017-0192

Heat kernel estimates for time fractional equations

Zhen Qing Chen
, Panki Kim
, Takashi Kumagai
, Jian Wang^*

^*Corresponding author for this work

University of Washington
Seoul National University
Kyoto University
Fujian Normal University

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

28 Citations (Scopus)

Abstract

In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time fractional equations in metric measure spaces.

Original language	English
Pages (from-to)	1163-1192
Number of pages	30
Journal	Forum Mathematicum
Volume	30
Issue number	5
DOIs	https://doi.org/10.1515/forum-2017-0192
Publication status	Published - 1 Sept 2018
Externally published	Yes

Keywords

Caputo derivative
Dirichlet form
heat kernel estimates
subordinator
time fractional equation

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title = "Heat kernel estimates for time fractional equations",

abstract = "In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time fractional equations in metric measure spaces.",

keywords = "Caputo derivative, Dirichlet form, heat kernel estimates, subordinator, time fractional equation",

author = "Chen, \{Zhen Qing\} and Panki Kim and Takashi Kumagai and Jian Wang",

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doi = "10.1515/forum-2017-0192",

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T1 - Heat kernel estimates for time fractional equations

AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Kumagai, Takashi

AU - Wang, Jian

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N2 - In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time fractional equations in metric measure spaces.

AB - In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time fractional equations in metric measure spaces.

KW - Caputo derivative

KW - Dirichlet form

KW - heat kernel estimates

KW - subordinator

KW - time fractional equation

UR - https://www.scopus.com/pages/publications/85042351318

U2 - 10.1515/forum-2017-0192

DO - 10.1515/forum-2017-0192

M3 - Article

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SN - 0933-7741

VL - 30

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EP - 1192

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 5

ER -

Heat kernel estimates for time fractional equations

Abstract

Keywords

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