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The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms

Haihua Lu;  Feng Wang;  Qiaoyun Jiang — 2011

Annales Polonici Mathematici

This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources u p ( x ₀ , t ) , vⁿ(x₀,t), local sources u m ( x , t ) , v q ( x , t ) , and weight functions a(x),b(x), on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases m,q ≤ 1 or m,q > 1, but also for m > 1 q < 1 or m < 1 q > 1.

Blow-up results for some reaction-diffusion equations with time delay

Hongliang Wang;  Yujuan Chen;  Haihua Lu — 2012

Annales Polonici Mathematici

We discuss the effect of time delay on blow-up of solutions to initial-boundary value problems for nonlinear reaction-diffusion equations. Firstly, two examples are given, which indicate that the delay can both induce and prevent the blow-up of solutions. Then we show that adding a new term with delay may not change the blow-up character of solutions.

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