An adaptive numerical method for the wave equation with a nonlinear boundary condition.
Ackleh, Azmy S., Deng, Keng, Derouen, Joel (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Ackleh, Azmy S., Deng, Keng, Derouen, Joel (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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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.
Assalé, Louis A., Boni, Théodore K., Firmin (2008)
Bulletin of TICMI
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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.
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 . We numerically investigate the blow-up rates of these solutions by using a numerical method which is recently proposed by the authors [3].