Blow-up results of a time fractional heat equation with a nonlinear Neumann boundary condition
Abstract
The study of blow-up problems for time Caputo fractional heat equations are of great wide-ranging interest for its multitude of applications and the fact that these kinds of problems are found in several areas of science and engineering. This article is concerned with the blow-up solutions of a time fractional heat equation subject to a nonlinear Neumann boundary condition of power type. Firstly, under some restricted conditions, it is proved that every positive solution blows up in finite time. Secondly, it is proved that the blow up phenomenon can only occurs at the boundary.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Nonlinear Partial Differential Equations
Fractional Differential Equations Solutions
Publication details
- Journal / source
- Tamkang Journal of Mathematics
- Volume
- 57
- Issue
- 1
- Pages
- 51–62
- Publication date
- 20 January 2026