Geodesic
On the existence of a solution to the Laplace equation with a nonlinear dynamic boundary condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 95-110 Cet article a éte moissonné depuis la source Math-Net.Ru

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M. O. Korpusov; A. G. Sveshnikov. On the existence of a solution to the Laplace equation with a nonlinear dynamic boundary condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 95-110. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a7/

[1] Tamm I. E., Osnovy teorii elektrichestva, Nauka, M., 1989

[2] Stretton Dzh. A., Teoriya elektromagnetizma, OGIZ, M., 1948

[3] Egorov I. E., Pyatkov S. G., Popov S. V., Neklassicheskie differentsialno-operatornye uravneniya, Nauka, Novosibirsk, 2000 | MR

[4] Sviridyuk G. A., “K obschei teorii polugrupp operatorov”, Uspekhi matem. nauk, 49:4 (1994), 47–74 | MR | Zbl

[5] Levine H. A., “Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $Pu_t=-Au+F(u)$”, Arch. Ration. Mech. and Analys., 51 (1973), 371–386 | MR | Zbl

[6] Gaevskii Kh., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[7] Kozhanov A. I., “Nachalno-kraevaya zadacha dlya uravnenii tipa obobschennogo uravneniya Bussineska s nelineinym istochnikom”, Matem. zametki, 64:1 (1999), 70–75 | MR

[8] Korpusov M. O., Pletner Yu. D., Sveshnikov A. G., “O kvazistatsionarnykh protsessakh v provodyaschikh sredakh bez dispersii”, Zh. vychisl. matem. i matem. fiz., 40:8 (2000), 1237–1249 | MR | Zbl

[9] Korpusov M. O., Sveshnikov A. G., “O razrushenii za konechnoe vremya resheniya nachalno-kraevoi zadachi dlya polulineinogo uravneniya sostavnogo tipa”, Zh. vychisl. matem. i matem. fiz., 40:11 (2000), 1716–1724 | MR | Zbl

[10] Korpusov M. O., “Globalnaya razreshimost i razrushenie za konechnoe vremya reshenii nelineinykh uravnenii psevdoparabolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 42:6 (2002), 849–866 | MR | Zbl

[11] Gladkov A. L., “Edinstvennost resheniya zadachi Koshi dlya nekotorykh kvazilineinykh psevdoparabolicheskikh uravnenii”, Matem. zametki, 60:3 (1996), 356–362 | MR | Zbl

[12] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR

[13] Gabov S. A., Novye zadachi matematicheskoi teorii voln, Fizmatgiz, M., 1998 | Zbl

[14] Amann H., Fila M., “A fujita-type theorem for the laplace equation with a dynamical boundary condition”, Acta Math. Univ. Comenianae, 66:2 (1997), 321–328 | MR | Zbl

[15] Fujita H., “On the blowing up of solutions to the Cauchy problem for $u_t=\Delta u+u^{1+\alpha}$”, J. Fac. Univ. Tokyo. Sect. IA, 13 (1966), 109–124 | MR | Zbl

[16] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | MR

[17] Vladimirov V. S., Uravneniya matematicheskoi fiziki, Nauka, M., 1988 | MR

[18] Maslennikova V. N., Differentsialnye uravneniya v chastnykh proizvodnykh, Izd-vo RUDN, M., 1997

[19] Dyachenko M. I., Ulyanov P. L., Mera i integral, Faktorial, M., 1998