On the substantiation of a projection method for the stationary Fokker–Planck equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 647-653 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A projection-type condition is discussed that is sufficient for the stationary Fokker–Planck equation $\Delta u-\operatorname{div}(u\mathbf f)=0$ to be solvable within a class of probability density functions. Based on existence theorems and estimates of positive solutions obtained by the author, a fairly large class of vector fields $\mathbf f$ satisfying this condition is proposed.
@article{ZVMMF_2011_51_4_a8,
     author = {A. I. Noarov},
     title = {On the substantiation of a~projection method for the stationary {Fokker{\textendash}Planck} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {647--653},
     year = {2011},
     volume = {51},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a8/}
}
TY  - JOUR
AU  - A. I. Noarov
TI  - On the substantiation of a projection method for the stationary Fokker–Planck equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 647
EP  - 653
VL  - 51
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a8/
LA  - ru
ID  - ZVMMF_2011_51_4_a8
ER  - 
%0 Journal Article
%A A. I. Noarov
%T On the substantiation of a projection method for the stationary Fokker–Planck equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 647-653
%V 51
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a8/
%G ru
%F ZVMMF_2011_51_4_a8
A. I. Noarov. On the substantiation of a projection method for the stationary Fokker–Planck equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 4, pp. 647-653. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_4_a8/

[1] Noarov A. I., “Ob odnom dostatochnom uslovii suschestvovaniya statsionarnogo resheniya uravneniya Fokkera–Planka”, Zh. vychisl. matem. i matem. fiz., 37:5 (1997), 587–598 | MR | Zbl

[2] Noarov A. I., “Chislennoe issledovanie uravneniya Fokkera–Planka”, Zh. vychisl. matem. i matem. fiz., 39:8 (1999), 1337–1347 | MR | Zbl

[3] Noarov A. I., “Otklik dinamicheskoi sistemy na maloe izmenenie pravoi chasti i konechnomernye analogi uravneniya Fokkera–Planka”, Zh. vychisl. matem. i matem. fiz., 45:7 (2005), 1237–1250 | MR | Zbl

[4] Noarov A. I., “Chislennaya stabilizatsiya sistemy Lorentsa malym vneshnim vozdeistviem”, Zh. vychisl. matem. i matem. fiz., 46:8 (2006), 1415–1422 | MR

[5] Noarov A. I., “K chislennoi optimizatsii nekotorykh dinamiko-stokhasticheskikh sistem”, Zh. vychisl. matem. i matem. fiz., 47:7 (2007), 1179–1186 | MR

[6] Noarov A. I., “O razreshimosti statsionarnykh uravnenii Fokkera–Planka, blizkikh k uravneniyu Laplasa”, Differents. ur-niya, 42:4 (2006), 521–530 | MR | Zbl

[7] Noarov A. I., “Obobschennaya razreshimost statsionarnogo uravneniya Fokkera–Planka”, Differents. ur-niya, 43:6 (2007), 813–819 | MR | Zbl

[8] Noarov A. I., “Odnoznachnaya razreshimost statsionarnogo uravneniya Fokkera–Planka v klasse polozhitelnykh funktsii”, Differents. ur-niya, 45:2 (2009), 191–202 | MR | Zbl

[9] Noarov A. I., “O nekotorykh diffuzionnykh protsessakh so statsionarnymi raspredeleniyami”, Teoriya veroyatnostei i ee primeneniya, 54:3 (2009), 589–598 | MR

[10] Khasminskii R. Z., Ustoichivost sistem differentsialnykh uravnenii pri sluchainykh vozmuscheniyakh ikh parametrov, Nauka, M., 1969 | MR

[11] Bogachev V. I., Rekner M., “Obobschenie teoremy Khasminskogo o suschestvovanii invariantnykh mer dlya lokalno integriruemykh snosov”, Teoriya veroyatnostei i ee primeneniya, 45:3 (2000), 417–436 | MR | Zbl