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

100%

Lu H., Wang F., Jiang Q.

Annales Polonici Mathematici

2011

tom 102

nr 2

187-203

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 $u^{p}(x₀,t)$, 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

100%

Wang H., Chen Y., Lu H.

Annales Polonici Mathematici

2012

tom 105

nr 1

21-29

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.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Lu H.

1 Chen Y.

1 Jiang Q.

1 Wang F.

1 Wang H.

1 2012

1 2011

Wyniki wyszukiwania

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

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