@article{ASENS_1986_4_19_4_519_0,
author = {Degond, Pierre},
title = {Global existence of smooth solutions for the {Vlasov-Fokker-Planck} equation in $1$ and $2$ space dimensions},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {519--542},
publisher = {Elsevier},
volume = {Ser. 4, 19},
number = {4},
year = {1986},
doi = {10.24033/asens.1516},
mrnumber = {88d:35168},
zbl = {0619.35087},
language = {en},
url = {http://www.numdam.org/articles/10.24033/asens.1516/}
}
TY - JOUR AU - Degond, Pierre TI - Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions JO - Annales scientifiques de l'École Normale Supérieure PY - 1986 SP - 519 EP - 542 VL - 19 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.24033/asens.1516/ DO - 10.24033/asens.1516 LA - en ID - ASENS_1986_4_19_4_519_0 ER -
%0 Journal Article %A Degond, Pierre %T Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions %J Annales scientifiques de l'École Normale Supérieure %D 1986 %P 519-542 %V 19 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.24033/asens.1516/ %R 10.24033/asens.1516 %G en %F ASENS_1986_4_19_4_519_0
Degond, Pierre. Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in $1$ and $2$ space dimensions. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 19 (1986) no. 4, pp. 519-542. doi : 10.24033/asens.1516. http://www.numdam.org/articles/10.24033/asens.1516/
[1] , Global existence of a weak solution of Vlasov's system of equations (USSR comput. Math. and Math. Phys., Vol. 15, 1975, pp. 131-143).
[2] and , Sur une équation d'évolution changeant de type (J. of functional analysis, 1968, pp. 352-367). | MR | Zbl
[3] and , Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data to appear in Ann. Inst. Henri-Poincaré ; Analyse non linéaire, Vol. 2, No. 2, 1985, pp. 101-118. | EuDML | Numdam | MR | Zbl
[4] , and , Remarks on the breakdown of smooth solutions for the 3.D Euler equations, Preprint, university of Berkeley. | Zbl
[5] , Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity, Internal Report No. 117, Centre de Mathématiques appliquées, Ecole Polytechnique, Paris. | Zbl
[6] and , Existence of solutions and diffusion approximation for a model Fokker-Planck equation of a monoenergetic plasma, Manuscript to appear in internal reports, Ecole Polytechnique. | Zbl
[7] , On the classical solutions of the initial value problem for the unmodified nonlinear Vlasov equation (Math. meth. in the appl. Sci, Vol. 3, 1981, pp. 229-248). | MR | Zbl
[8] and , An existence theorem for the unmodified Vlasov equation (Math. meth. in the appl. Sci., Vol. 1, 1979, pp. 530-554). | MR | Zbl
[9] , The Cauchy problem for the kinetic equation of Plasma (Amer. Math. Soc. Trans., Vol. 2-35, 1964, pp. 351-363). | Zbl
[10] , Equations différentielles opérationnelles et problèmes aux limites, Springer, Berlin, 1961. | Zbl
[11] , and , On the Vlasov-Fokker-Planck equation, preprint n° 77, Fachbereich Mathematik, Universitöt Kaiserlautern, January 1984. | MR
[12] , Topics is nonlinear analysis, Publications mathématiques de l'Université de Paris-Sud (Orsay), novembre 1978. | Zbl
[13] and , On the classical solution in the large in time of the two dimensional Vlasov equation (Osaka J. of math., Vol. 15, 1978, pp. 245-261). | MR | Zbl
[14] , Existence and uniqueness theory of the Vlasov equation, Internal report, Courant Institute, New York, October 1982.
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