Nonlocal elliptic problems
Krzywicki, Andrzej ; Nadzieja, Tadeusz
Banach Center Publications, Tome 51 (2000), p. 147-152 / Harvested from The Polish Digital Mathematics Library

Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem -Δφ=Mf(φ)/((Ωf(φ))p), φ|Ω=0 are given.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:209052
@article{bwmeta1.element.bwnjournal-article-bcpv52z1p147bwm,
     author = {Krzywicki, Andrzej and Nadzieja, Tadeusz},
     title = {Nonlocal elliptic problems},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {147-152},
     zbl = {0953.35040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv52z1p147bwm}
}
Krzywicki, Andrzej; Nadzieja, Tadeusz. Nonlocal elliptic problems. Banach Center Publications, Tome 51 (2000) pp. 147-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv52z1p147bwm/

[000] [A] J. J. Aly, Thermodynamics of a two-dimensional self-gravitating system, Physical Review E 49 (1994), 3771-3783.

[001] [B] F. Bavaud, Equilibrium properties of the Vlasov functional: the generalized Poisson-Boltzmann-Emden equation, Rev. Mod. Phys. 63 (1991), 129-148.

[002] [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. | Zbl 1023.35512

[003] [BT] J. W. Bebernes and P. Talaga, Nonlocal problems modelling shear banding, Comm. Appl. Nonlinear Analysis 3 (1996), 79-103. | Zbl 0858.35052

[004] [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. | Zbl 0814.35054

[005] [BKN] P. Biler, A. Krzywicki and T. Nadzieja, Self-interaction of Brownian particles coupled with thermodynamic processes, Reports Math. Physics 42 (1998), 359-372. | Zbl 1010.82028

[006] [BN1] P. Biler and T. Nadzieja, A class of nonlocal parabolic problems occurring in statistical mechanics, Colloq. Math. 66 (1993), 131-145. | Zbl 0818.35046

[007] [BN2] P. Biler and T. Nadzieja, Nonlocal parabolic problems in statistical mechanics, Nonlinear Analysis T. M. A. 30 (1997), 5343-5350. | Zbl 0892.35073

[008] [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. | Zbl 0817.35041

[009] [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. | Zbl 0745.76001

[010] [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. | Zbl 0895.35037

[011] [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. | Zbl 0665.76145

[012] [GW] M. Grüter and K. O. Widman, The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), 303-342. | Zbl 0485.35031

[013] [KN1] A. Krzywicki and T. Nadzieja, Poisson-Boltzmann equation in 3, Ann. Polon. Math. 54 (1991), 125-134. | Zbl 0733.35039

[014] [KN2] A. Krzywicki and T. Nadzieja, Some results concerning Poisson-Boltzmann equation, Zastosowania Matematyki 21 (1991), 265-272. | Zbl 0756.35029

[015] [KN3] A. Krzywicki and T. Nadzieja, A note on the Poisson-Boltzmann equation, Zastosowania Matematyki 21 (1993), 591-595. | Zbl 0780.35033

[016] [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.

[017] [LU] O. A. Ladyženskaja and N. N. Ural'ceva, Linear and quasilinear elliptic equations (in Russian), Moskva 1973.

[018] [S] R. F. Streater, A gas of Brownian particles in statistical dynamics, J. Stat. Phys. 88 (1997), 447-469. | Zbl 0939.82026

[019] [T] D. E. Tzanetis, Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating, 1-24, Preprint. | Zbl 0993.35018

[020] [W] G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992), 355-391. | Zbl 0774.76069