A single quenching point for a fractional heat equation based on the Riemann-Liouville fractional derivative with a nonlinear concentrate source

Boundary value problems

Panumart Sawangtong¹  Wannika Sawangtong² 

[1] Centre of Excellence in Mathematics, PERDO, Commission on Higher Education, Ministry of Education, Bangkok, Thailand;Department of Mathematics, Faculty of Science, Mahidol University, Bangkok, Thailand

关键词: quenching;    fractional heat equation;    Riemann-Liouville derivative;    existence and uniqueness;   

DOI  :  10.1186/s13661-017-0830-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper aims to study the quenching problem in a fractional heat equation with the Riemann-Liouville fractional derivative. The existence and uniqueness of a solution for the problem are obtained by transforming the problem to an equivalent integral equation. The condition for the quenching occurrence in a finite time is given. Furthermore, the quenching point set is shown.

【 授权许可】

CC BY