Global and exploding solutions in a model of self-gravitating systems. (English) Zbl 1043.85001
Summary: We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater’s energy-transport and the present models are also studied.
MSC:
| 85A05 | Galactic and stellar dynamics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35K57 | Reaction-diffusion equations |
| 82C21 | Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics |
| 35B45 | A priori estimates in context of PDEs |
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 35K55 | Nonlinear parabolic equations |
Keywords:
Chavanis-Sommeria-Robert model; mean field equations; drift-diffusion; energy-transport systems; finite time blow-up; asymptotics of solutionsReferences:
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