Abstract
This paper is concerned with a Coupled Reaction-diffusion system defined in a ball with homogeneous Dirichlet boundary conditions. Firstly, we studied the blow-up set showing that, under some conditions, the blow-up in this problem occurs only at a single point. Secondly, under some restricted assumptions on the reaction terms, we established the upper (lower) blow-up rate estimates. Finally, we considered the Ignition system in general dimensional space as an application to our results.
Highlights
It is well known that many phenomena in the world can be described using partial differential equations
This work is concerned with the blow-up properties of a Coupled Reaction-diffusion system defined in a ball with homogeneous Dirichlet boundary conditions:
It has been proved that the only blow-up point is and the upper blow-up rate estimates are as follows [6]: In this paper, under some conditions on the reaction terms, and, we prove that blow-up, in problem (1), occurs only at a single point
Summary
It is well known that many phenomena in the world can be described using partial differential equations. In [6], it was shown that the upper and lower blow-up rate estimates of this problem are as follows: For another special case of problem (1), where are of exponential type, we have (5). It has been proved that the only blow-up point is and the upper (lower) blow-up rate estimates are as follows [6]: In this paper, under some conditions on the reaction terms, and , we prove that blow-up, in problem (1), occurs only at a single point. We established the upper (lower) blow-up rate estimates In addition, the Ignition system [10] will be considered in a general dimensional space as an application to our result
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
