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

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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.

Boundary blow-up solutions for a cooperative system involving the p-Laplacian

100%

Chen L., Chen Y., Luo D.

Annales Polonici Mathematici

2013

tom 109

nr 3

297-310

We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_p u = g(u-αv), Δ_p v = f(v-βu)$ in a smooth bounded domain of $ℝ^N$, where $Δ_p$ is the p-Laplacian operator defined by $Δ_p u = div(|∇u|^{p-2} ∇u)$ with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Chen Y.

1 Chen L.

1 Lu H.

1 Luo D.

1 Wang H.

1 2013

1 2012

Wyniki wyszukiwania

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

Boundary blow-up solutions for a cooperative system involving the p-Laplacian