A nonlocal singular parabolic problem modelling gravitational interaction of particles

Advances in Differential Equations

Volumn 3, Issue 2, 1998, Pages 177-197

  Biler, Piotr ^a   Nadzieja, Tadeusz ^a  

^a INSTITUTE OF MATHEMATICS   (Poland)

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[No Author keywords available]

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EID: 0009127223     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. 1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Sup. Pisa, Ser. IV 22 (1995), 241-273.
2. P. Biler, Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions, Nonlinear Analysis T. M. A. 19 (1992), 1121-1136.
3. P. Biler, The Cauchy problem and self-similar solutions for a nonlinear parabolic equation, Studia Math. 114 (1995), 181-205.
4. P. Biler, Local and global solutions of a nonlinear nonlocal parabolic problem, Proceedings of the Banach Center minisemester "Nonlinear Analysis and Applications, Warsaw 1994", N. Kenmochi, M. Niezgódka, eds., Gakuto Int. Series Math. Sciences and Its Appl. 7 (1995), 49-66.
5. P. Biler, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III, Colloq. Math. 68 (1995), 229-239.
6. P. Biler, Growth and accretion of mass in an astrophysical model, Applicationes Math. 23 (1995), 179-189.
7. P. Biler, W. Hebisch, and T. Nadzieja, The Debye system: existence and long time behavior of solutions, Nonlinear Analysis T. M. A. 23 (1994), 1189-1209.
8. P. Biler, D. Hilhorst, and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, II, Colloq. Math. 67 (1994), 297-308.
9. P. Biler, T. Nadzieja, A class of nonlocal parabolic problems occuring in statistical mechanics, Colloq. Math. 66 (1993), 131-145.
10. P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I, Colloq. Math. 66 (1994), 319-334.
11. P. Biler and T. Nadzieja, Growth and accretion of mass in an astrophysical model, II, Applicationes Math. 23 (1995), 351-361.
12. P. Biler and T. Nadzieja, A singular problem in electrolytes theory, Math. Methods Appl. Sci., 20 (1997), 767-782.
13. L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Analysis T. M. A. 19 (1992), 581-597.
14. E. Caglioti, P.-L. Lions, C. Marchioro and M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description I, II, Comm. Math. Phys. 143, 174 (1992, 1995), 501-525, 229-260.
15. P. Cherrier, Meilleures constantes dans des inégalités relatives aux espaces de Sobolev, Bull. Sci. Math. 108 (1984), 225-262.
16. O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1988.
17. T. Nadzieja, A model of radially symmetric cloud of self-attracting particles, Applicationes Math. 23 (1995), 169-178.
18. M. Nagasawa, Schrödinger Equations and Diffusion Theory, Birkhäuser, 1993.
19. J. M. Rakotoson, A compactness lemma for quasilinear problems: application to parabolic equations, J. Funct. Anal. 106 (1992), 358-374.
20. G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
21. G. Wolansky, On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity, J. Analyse Math. 59 (1992), 251-272.