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

A nonlocal problem describing spherical system of stars

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.
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.   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.   Google Scholar

[3]

P. Biler, T. Nadzieja and R. Stańczy, Nonisothermal systems of self-attracting Fermi-Dirac particles,, Banach Center Publ., 66 (2004), 61.  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.   Google Scholar

[5]

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

[6]

J. Binney, S. Tremaine, Galactic Dynamics,, Princeton Univ. Press, (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, (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.   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.   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.   Google Scholar

[3]

P. Biler, T. Nadzieja and R. Stańczy, Nonisothermal systems of self-attracting Fermi-Dirac particles,, Banach Center Publ., 66 (2004), 61.  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.   Google Scholar

[5]

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

[6]

J. Binney, S. Tremaine, Galactic Dynamics,, Princeton Univ. Press, (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, (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.   Google Scholar

[1]

Qingfang Wang, Hua Yang. Solutions of nonlocal problem with critical exponent. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5591-5608. doi: 10.3934/cpaa.2020253

[2]

Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

[3]

Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. On existence and uniqueness properties for solutions of stochastic fixed point equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020320

[4]

Zhilei Liang, Jiangyu Shuai. Existence of strong solution for the Cauchy problem of fully compressible Navier-Stokes equations in two dimensions. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020348

[5]

Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020436

[6]

Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020469

[7]

Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020052

[8]

Monia Capanna, Jean C. Nakasato, Marcone C. Pereira, Julio D. Rossi. Homogenization for nonlocal problems with smooth kernels. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020385

[9]

Min Chen, Olivier Goubet, Shenghao Li. Mathematical analysis of bump to bucket problem. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5567-5580. doi: 10.3934/cpaa.2020251

[10]

Yuxia Guo, Shaolong Peng. A direct method of moving planes for fully nonlinear nonlocal operators and applications. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020462

[11]

Shao-Xia Qiao, Li-Jun Du. Propagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearity. Electronic Research Archive, , () : -. doi: 10.3934/era.2020116

[12]

Stefano Bianchini, Paolo Bonicatto. Forward untangling and applications to the uniqueness problem for the continuity equation. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020384

[13]

Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020383

[14]

Yichen Zhang, Meiqiang Feng. A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075

[15]

Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243

[16]

Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $ q $-integro-differential equations with three criteria. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020440

[17]

Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020453

[18]

Alberto Bressan, Sondre Tesdal Galtung. A 2-dimensional shape optimization problem for tree branches. Networks & Heterogeneous Media, 2020  doi: 10.3934/nhm.2020031

[19]

Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020075

[20]

Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]