On the regularity of weak solutions to space-time fractional stochastic heat equations

被引：7

作者：

Zou, Guang-an ^{[1
]}

Lv, Guangying ^{[1
]}

Wu, Jiang-Lun ^{[2
]}

机构：

[1] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China

[2] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

来源：

STATISTICS & PROBABILITY LETTERS | 2018年 / 139卷

基金：

中国国家自然科学基金;

关键词：

Space-time fractional derivative; Stochastic heat equations; Weak solutions; Regularity properties;

D O I：

10.1016/j.spl.2018.04.006

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This study is concerned with the space-time fractional stochastic heat-type equations driven by multiplicative noise, which can be used to model the anomalous heat diffusion in porous media with random effects with thermal memory. We first deduce the weak solutions to the given problem by means of the Laplace transform and Mittag-Leffler function. Using the fractional calculus and stochastic analysis theory, we further prove the pathwise spatial-temporal regularity properties of weak solutions to this type of SPDEs in the framework of Bochner spaces. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：84 / 89

页数：6

共 50 条

[1] REGULARITY OF SOLUTIONS TO SPACE-TIME FRACTIONAL WAVE EQUATIONS: A PDE APPROACH
Otarola, Enrique
Salgado, Abner J.
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (05) : 1262 - 1293
[2] Stochastic classical solutions for space-time fractional evolution equations on a bounded domain
Toniazzi, Lorenzo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 469 (02) : 594 - 622
[3] Stochastic solution of space-time fractional diffusion equations
Meerschaert, MM
Benson, DA
Scheffler, HP
Baeumer, B
[J]. PHYSICAL REVIEW E, 2002, 65 (04): : 4
[4] Space-time fractional stochastic partial differential equations
Mijena, Jebessa B.
Nane, Erkan
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (09) : 3301 - 3326
[5] Space-time regularity of solutions of the parabolic stochastic cauchy problem
Dettweiler, Johanna
Weis, Lutz
van Neerven, Jan
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2006, 24 (04) : 843 - 869
[6] On space-time regularity for the stochastic heat equation on Lie groups
Tindel, S
Viens, F
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 169 (02) : 559 - 603
[7] Existence and space-time regularity for stochastic heat equations on p.c.f. fractals
Hambly, Ben
Yang, Weiye
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2018, 23
[8] Space-time coupled evolution equations and their stochastic solutions
Herman, John
Johnston, Ifan
Toniazzi, Lorenzo
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2020, 25 : 1 - 21
[9] Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise
Herrell, Randall
Song, Renming
Wu, Dongsheng
Xiao, Yimin
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2020, 38 (04) : 747 - 768
[10] Asymptotic properties of some space-time fractional stochastic equations
Mohammud Foondun
Erkan Nane
[J]. Mathematische Zeitschrift, 2017, 287 : 493 - 519

← 1 2 3 4 5 →