On blow-up at space infinity for semilinear heat equations

Giga, Y.; Umeda, N.

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Displaying similar documents to “On blow-up at space infinity for semilinear heat equations”

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.

The blow-up rate for a semilinear parabolic equation with a nonlinear boundary condition.

Rossi, J.D. (1998)

Acta Mathematica Universitatis Comenianae. New Series

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Similarity stabilizes blow-up

Steve Schochet (1999)

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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.

Recent progress on the blow-up problem of Zakharov equations

Frank Merle (1995)

Journées équations aux dérivées partielles

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Blow-up behavior in nonlocal vs local heat equations

Philippe Souplet (2000)

Banach Center Publications

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We present some recent results on the blow-up behavior of solutions of heat equations with nonlocal nonlinearities. These results concern blow-up sets, rates and profiles. We then compare them with the corresponding results in the local case, and we show that the two types of problems exhibit "dual" blow-up behaviors.

Simultaneous versus nonsimultaneous blowup for a system of heat equations coupled boundary flux.

Fan, Mingshu, Du, Lili (2007)

Boundary Value Problems [electronic only]

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