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

  • 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
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 inĀ  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.

Published
2020-01-27
How to Cite
Rasheed, M. A., & Chlebik, M. (2020). Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions. Iraqi Journal of Science, 61(1), 147-152. https://doi.org/10.24996/ijs.2020.61.1.17
Section
Mathematics