Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions

Maan A. Rasheed; Miroslav Chlebik

doi:10.24996/ijs.2020.61.1.17

Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions

Authors

Maan A. Rasheed Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
Miroslav Chlebik Department of Mathematics, School of Physical and Mathematical Sciences, University of Sussex, UK

DOI:

https://doi.org/10.24996/ijs.2020.61.1.17

Keywords:

Heat equation, Neumann boundary conditions, Blow-up set, Blow-up rate estimate, Green function

Abstract

This paper deals with the blow-up properties of positive solutions to a parabolic system of two heat equations, defined on a ball in associated with coupled Neumann boundary conditions of exponential type. The upper bounds of blow-up rate estimates are derived. Moreover, it is proved that the blow-up in this problem can only occur on the boundary.

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Published

2020-01-27

Issue

Vol 61 No 1 (2020)

Section

Mathematics

How to Cite

Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions. (2020). Iraqi Journal of Science, 61(1), 147-152. https://doi.org/10.24996/ijs.2020.61.1.17