Remarks on the wave equation with a nonlinear term with respect to the velocity
Haraux, A. (1992)
Portugaliae mathematica
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Displaying similar documents to “A remark on the blow-up of the solutions of a partial differential equation.”
Remarks on the wave equation with a nonlinear term with respect to the velocity
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.
Recent progress on the blow-up problem of Zakharov equations
Frank Merle (1995)
Journées équations aux dérivées partielles
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On the well posedness of a system of balance laws with data
Marta Lewicka (1999)
Rendiconti del Seminario Matematico della Università di Padova
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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.