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2000 | 52 | 1 | 147-152
Tytuł artykułu

Nonlocal elliptic problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem $-Δφ = M f(φ)/((∫_{Ω} f(φ))^p)$, $φ|_{𝜕Ω}=0$ are given.
Rocznik
Tom
52
Numer
1
Strony
147-152
Opis fizyczny
Daty
wydano
2000
Twórcy
  • Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
  • [A] J. J. Aly, Thermodynamics of a two-dimensional self-gravitating system, Physical Review E 49 (1994), 3771-3783.
  • [B] F. Bavaud, Equilibrium properties of the Vlasov functional: the generalized Poisson-Boltzmann-Emden equation, Rev. Mod. Phys. 63 (1991), 129-148.
  • [BL] J. W. Bebernes and A. A. Lacey, Global existence and finite-time blow-up for a class of nonlocal parabolic problems, Adv. Diff. Equations 2 (1997), 927-953.
  • [BT] J. W. Bebernes and P. Talaga, Nonlocal problems modelling shear banding, Comm. Appl. Nonlinear Analysis 3 (1996), 79-103.
  • [BHN] P. Biler, W. Hebisch and T. Nadzieja, The Debye system: existence and large time behavior of solutions, Nonlinear Analysis T.M.A. 23 (1994), 1189-1209.
  • [BKN] P. Biler, A. Krzywicki and T. Nadzieja, Self-interaction of Brownian particles coupled with thermodynamic processes, Reports Math. Physics 42 (1998), 359-372.
  • [BN1] P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, Colloq. Math. 66 (1993), 131-145.
  • [BN2] P. Biler and T. Nadzieja, Nonlocal parabolic problems in statistical mechanics, Nonlinear Analysis T. M. A. 30 (1997), 5343-5350.
  • [BN3] 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.
  • [CLMP] 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, Comm. Math. Phys. 143 (1992), 501-525.
  • [C] J. A. Carrillo, On a nonlocal elliptic equation with decreasing nonlinearity arising in plasma physics and heat conduction, Nonlinear Analysis T. M. A. 32 (1998), 97-115.
  • [GL] D. Gogny and P. L. Lions, Sur les états d'équilibre pour les densités électroniques dans les plasmas, Math. Modelling and Numerical Analysis, 23 (1989), 137-153.
  • [GW] M. Grüter and K. O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), 303-342.
  • [KN1] A. Krzywicki and T. Nadzieja, Poisson-Boltzmann equation in $ℝ^3$, Ann. Polon. Math. 54 (1991), 125-134.
  • [KN2] A. Krzywicki and T. Nadzieja, Some results concerning Poisson-Boltzmann equation, Zastosowania Matematyki 21 (1991), 265-272.
  • [KN3] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, Zastosowania Matematyki 21 (1993), 591-595.
  • [L] A. A. Lacey, Thermal runaway in a nonlocal problem modelling Ohmic heating: Part I: Model derivation and some special cases, Euro. J. Appl. Math. 6 (1995), 129-148.
  • [LU] O. A. Ladyženskaja and N. N. Ural'ceva, Linear and quasilinear elliptic equations (in Russian), Moskva 1973.
  • [S] R. F. Streater, A gas of Brownian particles in statistical dynamics, J. Stat. Phys. 88 (1997), 447-469.
  • [T] D. E. Tzanetis, Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating, 1-24, Preprint.
  • [W] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv52z1p147bwm
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