Numerical analysis of semilinear parabolic problems with blow-up solutions.

C. Bandle; H. Brunner

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Full discretization of some reaction diffusion equation with blow up

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This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

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On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order

Théodore K. Boni (2000)

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In questo lavoro sotto queste ipotesi si ottengono alcune condizioni di non esistenza e di esistenza delle soluzioni per alcuni sistemi parabolici semilineari del secondo ordine. Inoltre si studia il comportamento asintotico di alcune soluzioni.

Global existence and blow-up for a completely coupled Fujita type system

Joanna Rencławowicz (2000)

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The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form $u_{i t} = Δ u_{i} + u_{i + 1}^{p_{i}}, i = 1, . . ., m - 1,$ $u_{m t} = Δ u_{m} + u_{1}^{p_{m}}, x \in ℝ^{N}, t > 0,$ with nonnegative, bounded, continuous initial values and positive numbers $p_{i}$ . The dependence on $p_{i}$ of the length of existence time (its finiteness or infinitude) is established.

The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation

Juan Luis Vázquez (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.