一类分数阶随机热方程解的Hölder连续性

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (2): 159-165.

一类分数阶随机热方程解的Hölder连续性

刘洋, 吴克晴^*, 冯源

江西理工大学理学院, 江西赣州 341000

收稿日期:2023-08-16 出版日期:2025-04-28 发布日期:2025-04-29
通讯作者: 吴克晴(1972-),男,江西鹰潭人,博士,副教授.Email:wkq622@126.com
基金资助:
国家自然科学基金(61364015)

Hölder continuity of solutions for a class of fractional order stochastic heat equations

LIU Yang, WU Ke-qing, FENG Yuan

School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China

Received:2023-08-16 Online:2025-04-28 Published:2025-04-29

摘要/Abstract

摘要： 研究一类受噪声驱动影响的分数阶随机热方程解的Hölder连续性,方程中带有分数阶微分算子和噪声随机项,利用初值条件的特性和格林函数定义了解的形式,通过Picard迭代法和 Kolomogorov连续性定理得到了解的存在性和Hölder连续性,给出一个例子验证了所得结果.

关键词: 分数阶随机热方程, 噪声, Green’函数, Hölder连续性

Abstract: The Holder continuity is studied of solutions to a class of fractional stochastic heat equations driven by space-time white noises. With fractional differential operators and random noise terms in the equation, the form of the solution is defined by the characteristics of the initial value conditions and the Green’s function, the existence and Holder continuity of solutions are obtained by Picard iteration method and Kolomogorov continuity theorem. An example is given to verify the results.

Key words: fractional-order stochastic heat equation, noise, Green’s function, Hö, lder continuity

中图分类号:

O241.82

刘洋, 吴克晴, 冯源. 一类分数阶随机热方程解的Hölder连续性[J]. 兰州理工大学学报, 2025, 51(2): 159-165.

LIU Yang, WU Ke-qing, FENG Yuan. Hölder continuity of solutions for a class of fractional order stochastic heat equations[J]. Journal of Lanzhou University of Technology, 2025, 51(2): 159-165.

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