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October  2014, 19(8): 2417-2423. doi: 10.3934/dcdsb.2014.19.2417

A nonlocal problem describing spherical system of stars

Marcin Bugdoł 1, and  Tadeusz Nadzieja 1,

1. 

Institute of Mathematics and Computer Science, Opole University, ul. Oleska 48, 45-052 Opole, Poland, Poland

Received  March 2014 Revised  April 2014 Published  August 2014

We prove in this note the existence and uniqueness of solutions of a nonlocal problem appearing as a model of galaxy in early stage of evolution. Some properties of solutions are also given.
Keywords: Nonlocal and nonliner problem, model of galaxy., existence of solutions.
Mathematics Subject Classification: Primary: 34A12; Secondary: 85A1.
Citation: Marcin Bugdoł, Tadeusz Nadzieja. A nonlocal problem describing spherical system of stars. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2417-2423. doi: 10.3934/dcdsb.2014.19.2417
References:
[1]

T. A. Agekyan, Spherical systems of stars and galaxies in early stage of evolution, (Russian) Vestnik Leningrad Univ., I (1962), 153-161. Google Scholar

[2]

P. Biler and T. Nadzieja, Structure of steady states for Streater's energy-transport models of gravitating particles, Topological Methods in Nonlinear Analysis, 19 (2002), 283-301.  Google Scholar

[3]

P. Biler, T. Nadzieja and R. Stańczy, Nonisothermal systems of self-attracting Fermi-Dirac particles, Banach Center Publ., 66 (2004), 61-78. doi: 10.4064/bc66-0-5.  Google Scholar

[4]

P. Biler, Ph. Laurençot and T. Nadzieja, On an evolution system describing self-gravitating Fermi-Dirac particles, Adv. Diff.Eq., 9 (2004), 563-586.  Google Scholar

[5]

P. Biler and R. Stańczy, Nonlinear diffusion models for self-gravitating particles, Intern. Ser. Numer. Math, 154 (2007), 107-116. doi: 10.1007/978-3-7643-7719-9_11.  Google Scholar

[6]

J. Binney, S. Tremaine, Galactic Dynamics, Princeton Univ. Press, Princeton, 1987. doi: 10.1063/1.2811635.  Google Scholar

[7]

A. M. Friedman and V. L. Polyachenko, Physics of Gravitating Systems I: Equilibrium and Stability, Springer, New York, 1984. doi: 10.1007/978-3-642-87833-6.  Google Scholar

[8]

A. Krzywicki and T. Nadzieja, Nonlocal elliptic problems, Banach Center Publ., 52 (2000), 147-152.  Google Scholar

show all references

References:
[1]

T. A. Agekyan, Spherical systems of stars and galaxies in early stage of evolution, (Russian) Vestnik Leningrad Univ., I (1962), 153-161. Google Scholar

[2]

P. Biler and T. Nadzieja, Structure of steady states for Streater's energy-transport models of gravitating particles, Topological Methods in Nonlinear Analysis, 19 (2002), 283-301.  Google Scholar

[3]

P. Biler, T. Nadzieja and R. Stańczy, Nonisothermal systems of self-attracting Fermi-Dirac particles, Banach Center Publ., 66 (2004), 61-78. doi: 10.4064/bc66-0-5.  Google Scholar

[4]

P. Biler, Ph. Laurençot and T. Nadzieja, On an evolution system describing self-gravitating Fermi-Dirac particles, Adv. Diff.Eq., 9 (2004), 563-586.  Google Scholar

[5]

P. Biler and R. Stańczy, Nonlinear diffusion models for self-gravitating particles, Intern. Ser. Numer. Math, 154 (2007), 107-116. doi: 10.1007/978-3-7643-7719-9_11.  Google Scholar

[6]

J. Binney, S. Tremaine, Galactic Dynamics, Princeton Univ. Press, Princeton, 1987. doi: 10.1063/1.2811635.  Google Scholar

[7]

A. M. Friedman and V. L. Polyachenko, Physics of Gravitating Systems I: Equilibrium and Stability, Springer, New York, 1984. doi: 10.1007/978-3-642-87833-6.  Google Scholar

[8]

A. Krzywicki and T. Nadzieja, Nonlocal elliptic problems, Banach Center Publ., 52 (2000), 147-152.  Google Scholar

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