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@article{AA_2013_25_1_a2, author = {O. A. Manita and S. V. Shaposhnikov}, title = {Nonlinear parabolic equations for measures}, journal = {Algebra i analiz}, pages = {64--93}, publisher = {mathdoc}, volume = {25}, number = {1}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2013_25_1_a2/} }
O. A. Manita; S. V. Shaposhnikov. Nonlinear parabolic equations for measures. Algebra i analiz, Tome 25 (2013) no. 1, pp. 64-93. http://geodesic.mathdoc.fr/item/AA_2013_25_1_a2/
[1] Belopolskaya Ya. I., “Veroyatnostnyi podkhod k resheniyu sistem nelineinykh parabolicheskikh uravnenii”, Teoriya veroyatnostei i ee primeneniya, 49:4 (2004), 625–652 | DOI | MR | Zbl
[2] Bogachev V. I., Krylov N. V., Rëkner M., “Ellipticheskie i parabolicheskie uravneniya dlya mer”, Uspekhi mat. nauk, 64:6 (2009), 5–116 | DOI | MR | Zbl
[3] Bogachev V. I., Rëkner M., Shaposhnikov S. V., “Nelineinye evolyutsionnye i transportnye uravneniya dlya mer”, Dokl. RAN, 429:1 (2009), 7–11 | MR | Zbl
[4] Bogachev V. I., Osnovy teorii mery, v. 1, 2, 2-e izd., NITs RKhD, M.–Izhevsk, 2006
[5] Daletskii Yu. L., Fomin S. V., Mery i differentsialnye uravneniya v beskonechnomernykh prostranstvakh, Nauka, M., 1983 | MR
[6] Daletskii Yu. L., “Beskonechnomernye ellipticheskie operatory i svyazannye s nimi parabolicheskie uravneniya”, Uspekhi mat. nauk, 22:4 (1967), 3–54 | MR | Zbl
[7] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, Editorial URSS, M., 2004
[8] Dobrushin R. L., “Uravneniya Vlasova”, Funkts. anal. i ego pril., 13:2 (1979), 48–58 | MR | Zbl
[9] Kozlov V. V., “Obobschennoe kineticheskoe uravnenie Vlasova”, Uspekhi mat. nauk, 63:4 (2008), 93–130 | DOI | MR | Zbl
[10] Kozlov V. V., “Kineticheskoe uravnenie Vlasova, dinamika sploshnykh sred i turbulentnost”, Nelineinaya dinamika, 6:3 (2010), 489–512
[11] Mitidieri E., Pokhozhaev S. I., Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh, Tr. Mat. in-ta RAN, 234, 2001, 383 pp. | MR | Zbl
[12] Mitidieri E., Pokhozhaev S. I., “Liuvillevy teoremy dlya nekotorykh klassov nelineinykh nelokalnykh zadach”, Tr. Mat. in-ta RAN, 248, 2005, 164–184 | MR | Zbl
[13] Oleinik O. A., Radkevich E. V., Uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi, MGU, M., 2010
[14] Tonoyan L. G., “Nelineinye ellipticheskie uravneniya dlya mer”, Dokl. RAN, 439:2 (2011), 174–177 | MR | Zbl
[15] Shaposhnikov S. V., “O edinstvennosti veroyatnostnogo resheniya zadachi Koshi dlya uravneniya Fokkera–Planka–Kolmogorova”, Teoriya veroyatnostei i ee primeneniya, 56:1 (2011), 77–99 | DOI | MR
[16] Ambrosio L., “Transport equation and Cauchy problem for BV vector fields”, Invent. Math., 158 (2004), 227–260 | DOI | MR | Zbl
[17] Ambrosio L., “Transport equation and Cauchy problem for non-smooth vector fields”, Calculus of Variations and Nonlinear Partial Differential Equations, Lecture Notes in Math., 1927, Springer, Berlin, 2008, 1–41 | DOI | MR
[18] Bertozzi A. L., Carrillo J. A., Laurent T., “Blow-up in multidimensional aggregation equations with mildly singular interaction kernels”, Nonlinearity, 22 (2009), 683–710 | DOI | MR | Zbl
[19] Bogachev V. I., Da Prato G., Röckner M., “On parabolic equations for measures”, Comm. Partial Differential Equations, 33 (2008), 397–418 | DOI | MR | Zbl
[20] Bogachev V. I., Da Prato G., Röckner M., Shaposhnikov S. V., “Nonlinear evolution equations for measures on infinite dimensional spaces”, Stochastic Partial Differential Equations and Applications. Quaderni di Matematica, 25 (2010), 51–64 | MR
[21] Bogachev V. I., Röckner M., Shaposhnikov S. V., “On uniqueness problems related to the Fokker–Planck–Kolmogorov equations for measures”, J. Math. Sci. (New York), 179:1 (2011), 7–47 | DOI | MR
[22] Carrillo J. A., McCann R. J., Villani C., “Kinetic equilibration rates for granular media and related equations: entropy, dissipation and mass transportation estimates”, Rev. Mat. Iberoamericana, 19 (2003), 971–1018 | DOI | MR | Zbl
[23] Carrillo J. A., DiFrancesco M., Figalli A., Laurent T., Slepčev D., “Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations”, Duke Math. J., 156:2 (2011), 229–271 | DOI | MR | Zbl
[24] DiPerna R. J., Lions P.-L., “Ordinary differential equations, transport theory and Sobolev spaces”, Invent. Math., 98 (1989), 511–547 | DOI | MR | Zbl
[25] Funaki T., “A certain class of diffusion processes associated with nonlinear parabolic equations”, Z. Wahrsch. Verw. Gebiete, 67 (1984), 331–348 | DOI | MR | Zbl
[26] Li H., Toscani G., “Long-time asymptotics of kinetic models of granular flows”, Arch. Ration. Mech. Anal., 172 (2004), 407–428 | DOI | MR | Zbl
[27] Lorenz T., Mutational analysis, A joint framework for Cauchy problems in and beyond vector spaces, Lecture Notes in Math., 1996, Springer-Verlag, Berlin, 2010 | DOI | MR | Zbl
[28] Maniglia S., “Probabilistic representation and uniqueness results for measure-valued solutions of transport equations”, J. Math. Pures Appl. (9), 87 (2007), 601–626 | MR | Zbl
[29] Stroock D. W., Varadhan S. R. S., Multidimensional diffusion processes, Grundlehren Math. Wiss., 233, Springer-Verlag, Berlin–New York, 1979 | MR | Zbl