Global and exploding solutions in a model of self-gravitating systems |
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Authors: | Piotr Biler |
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Institution: | Instytut Matematyki, Uniwersytet Wroc?awski, pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland; Instytut Matematyki, Uniwersytet Zielonogórski, ul. Podgórna 50, 65-246 Zielona Góra, Poland |
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Abstract: | 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. |
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Keywords: | Chavanis-Sommeria-Robert model mean field equations drift-diffusion and energy-transport systems finite time blow-up of solutions asymptotics of solutions |
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