Abstract
This paper deals with a parabolic reaction-diffusion system with a nonlinear absorption term, meanwhile the two equations of the system coupled via nonlinear boundary flux which obey different laws. Under the hypothesis condition of the initial data, we get the sufficient and necessary conditions under which there exist initial data such that non-simultaneous blow-up occurs.
Highlights
1 Introduction and main results In this paper, we focus our attention on the non-simultaneous blow-up phenomenon of the following reaction-diffusion system with two parabolic equations coupled via nonlinear boundary flux, and one equation with a nonlinear absorption term:
We can set the initial data v large enough such that T satisfies
Summary
. In Section we will consider the sufficient and necessary conditions of u blowing up while v keeps bounded, which will be written as a lemma. In Section , the sufficient and necessary conditions of v blowing up while u remains bounded will be researched, in order to complete the proof of Theorem . ), if any of the following conditions holds: ( ) α > μ, ( ) β > , ( ) pq > β(α – μ), the solutions of system
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