1. Properties of non-simultaneous blow-up in heat equations coupled via different localized sources
- Author
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Liu, Bingchen and Li, Fengjie
- Subjects
- *
BLOWING up (Algebraic geometry) , *HEAT equation , *LOCALIZATION theory , *DIRICHLET problem , *NONNEGATIVE matrices , *MATHEMATICAL analysis - Abstract
Abstract: This paper deals with u t =Δu + u m (x, t)e pv(0,t), v t =Δv + u q (0, t)e nv(x,t), subject to homogeneous Dirichlet boundary conditions. The complete classification on non-simultaneous and simultaneous blow-up is obtained by four sufficient and necessary conditions. It is interesting that, in some exponent region, large initial data u 0(v 0) leads to the blow-up of u(v), and in some betweenness, simultaneous blow-up occurs. For all of the nonnegative exponents, we find that u(v) blows up only at a single point if m >1(n >0), while u(v) blows up everywhere for 0⩽ m ⩽1 (n =0). Moreover, blow-up rates are considered for both non-simultaneous and simultaneous blow-up solutions. [Copyright &y& Elsevier]
- Published
- 2010
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