PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 26 | 1 | 107-119
Tytuł artykułu

On a nonlocal elliptic problem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study stationary solutions of the system $u_t = ∇ ((m-1)/m ∇u^m + u∇φ)$, m => 1, Δφ = ±u, defined in a bounded domain Ω of $ℝ^n$. The physical interpretation of the above system comes from the porous medium theory and semiconductor physics.
Rocznik
Tom
26
Numer
1
Strony
107-119
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-10-17
poprawiono
1998-11-26
Twórcy
  • Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] G. I. Barenblatt, V. M. Entov and V. M. Ryzhik, Theory of Fluid Flows Through Natural Rocks, Kluwer, Dordrecht, 1990.
  • [2] J.-M. Bony, Principe du maximum, inégalité de Harnack, et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier (Grenoble) 19 (1969), no. 1, 277-304.
  • [3] P. Biler, Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary condition, Nonlinear Anal. 19 (1992), 229-239.
  • [4] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and large time behavior of solutions, ibid. 23 (1994), 1189-1209.
  • [5] P. Biler, D. Hilhorst and T. Nadzieja,
  • [E]xistence and nonexistence of solutions for a model of gravitational interaction of particles, II, Colloq. Math. 67 (1994), 297-308.
  • [6] P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, ibid. 66 (1993), 131-145.
  • [7] P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, I, ibid. 66 (1994), 319-334.
  • [8] P. Biler and T. Nadzieja, Nonlocal parabolic problems in statistical mechanics, Nonlinear Anal. 30 (1997), 5343-5350.
  • [9] P. Biler and T. Nadzieja, A singular problem in electrolytes theory, Math. Methods Appl. Sci. 20 (1997), 767-782.
  • [10] P. Biler and T. Nadzieja, A nonlocal singular parabolic problem modelling gravitational interaction of particles, Adv. Differential Equations 3 (1998), 177-197.
  • [11] P. Biler, T. Nadzieja and A. Raczyński, Nonlinear singular parabolic equations, in: Reaction-Diffusion Systems (Trieste, 1995), Lecture Notes in Pure and Appl. Math. 194, G. Caristi and E. Mitidieri (eds.), Dekker, 1998, 21-36.
  • [12] P. Debye und E. Hückel, Zur Theorie der Electrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen, Phys. Z. 24 (1923), 185-217.
  • [13] A. Jüngel, On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci. 5 (1994), 677-703.
  • [14] A. Krzywicki and T. Nadzieja, Poisson-Boltzmann equation in $ℝ^3$, Ann. Polon. Math. 54 (1991), 125-134.
  • [15] A. Krzywicki and T. Nadzieja, A nonstationary problem in the theory of electrolytes, Quart. Appl. Math. 50 (1992), 105-107.
  • [16] P. A. Markowich, C. A. Ringhofer and C. Schmeiser, Semiconductor Equations, Springer, Wien-New York, 1990.
  • [17] T. Nadzieja, A model of radially symmetric cloud of self-attracting particles, Appl. Math. (Warsaw) 23 (1995), 169-178.
  • [18] T. Nadzieja and A. Raczyński, A singular radially symmetric problem in electrolytes theory, ibid. 25 (1998), 101-112.
  • [19] C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
  • [20] M. Struwe, Variational Methods, Springer, New York, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv26i1p107bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.