Displaying similar documents to “Growth and accretion of mass in an astrophysical model, II”

Existence and nonexistence of solutions for a model of gravitational interaction of particles, II

Piotr Biler, Danielle Hilhorst, Tadeusz Nadzieja (1994)

Colloquium Mathematicae

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We study the existence and nonexistence in the large of radial solutions to a parabolic-elliptic system with natural (no-flux) boundary conditions describing the gravitational interaction of particles. The blow-up of solutions defined in the n-dimensional ball with large initial data is connected with the nonexistence of radial stationary solutions with a large mass.

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.

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*.

Asymptotic self-similar blow-up for a model of aggregation

Ignacio Guerra (2004)

Banach Center Publications

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In this article we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M. P. Brenner et al. 1999, Nonlinearity 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between...