Displaying similar documents to “Asymptotic self-similar blow-up for a model of aggregation”

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.

Global existence versus blow up for some models of interacting particles

Piotr Biler, Lorenzo Brandolese (2006)

Colloquium Mathematicae

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We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.

Growth and accretion of mass in an astrophysical model, II

Piotr Biler, Tadeusz Nadzieja (1995)

Applicationes Mathematicae

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Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

Marras, M. (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35K55, 35K60. We investigate the blow-up of the solutions to a nonlinear parabolic system with Robin boundary conditions and time dependent coefficients. We derive sufficient conditions on the nonlinearities and the initial data in order to obtain explicit lower and upper bounds for the blow up time t*.

Self-similarity in chemotaxis systems

Yūki Naito, Takashi Suzuki (2008)

Colloquium Mathematicae

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We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.