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Displaying similar documents to “Numerical blow-up for the p -Laplacian equation with a nonlinear source”

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.

Similarity stabilizes blow-up

Steve Schochet (1999)

Journées équations aux dérivées partielles

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The blow-up of solutions to a quasilinear heat equation is studied using a similarity transformation that turns the equation into a nonlocal equation whose steady solutions are stable. This allows energy methods to be used, instead of the comparison principles used previously. Among the questions discussed are the time and location of blow-up of perturbations of the steady blow-up profile.

Numerical study on the blow-up rate to a quasilinear parabolic equation

Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo

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In this paper, we consider the blow-up solutions for a quasilinear parabolic partial differential equation u t = u 2 ( u x x + u ) . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].