Abstract
In this paper, we study the simultaneous and non-simultaneous blow-up problem for a system of two nonlinear diffusion equations in a bounded interval, coupled at the boundary in a nonlinear way. Under certain hypotheses on the initial data and parameters, we prove that non-simultaneous blow-up is possible. Moreover, we get some conditions on which simultaneous blow-up must occur, as well as the non-simultaneous blow-up conditions for every initial data. Furthermore, we get a result on the coexistence of both simultaneous and non-simultaneous blow-ups.
Highlights
1 Introduction and main results In this paper, we study the nonlinear parabolic system ut =xx + λ uα, vt =xx + λ vβ, (x, t) ∈ DT = (, ) × (, T), ( . )
In [ ], Song and Zheng considered the blow-up conditions of the following problem:
They found some conditions under which u blows up and v remains bounded for every initial data
Summary
They found some conditions under which u blows up and v remains bounded for every initial data. There exists initial data (u , v ) such that v blows up at a finite time T , while u remains bounded up to T.
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