Geodesic
Method of Galyorkin for nonlinear Sobolev type equations
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2008), pp. 10-15 
R. Lotfikar. Method of Galyorkin for nonlinear Sobolev type equations. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2008), pp. 10-15. http://geodesic.mathdoc.fr/item/UZERU_2008_3_a1/
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     author = {R. Lotfikar},
     title = {Method of {Galyorkin} for nonlinear {Sobolev} type equations},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/UZERU_2008_3_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the following initial boundary value problem is considered: $$\left\{\begin{array}{l} L\left(\frac{\partial u(t,x)}{\partial t}\right)+Mu(t,x)=f(t,x),\\ u(0,x)=u_0(x),\\ D^{\gamma}u\Big|_{\tilde A}=0, |\gamma|,\end{array}\right.$$ $L$ and $M$ are nonlinear differential operators. It is proved that if $L$ and $M$ satisfy to some conditions, then the sequence constructed by solutions of Galyorkin’s equations for this problem is convergence to the week solution of the problem

[1] R. A. Aleksandryan, “Spektralnye svoistva operatorov, porozhdennykh sistemami differentsialnykh uravnenii tipa S. L. Soboleva”, Tr. MMO, 9, GIFML, M., 1960, 455–505 | MR | Zbl

[2] S. A. Galpern, “Zadacha Koshi dlya obschikh sistem lineinykh uravnenii s chastnymi proizvodnymi”, Tr. MMO, 9, GIFML, M., 1960, 401–423 | MR | Zbl

[3] R. A. Aleksandryan, Yu. M. Berezanskii, V. A. Ilin, A.G. Kostjucenko, “Some questions in spectral theory for partial differential equations”, Amer. Math. Soc. Transltions: Series II, 105, 1976, 1-53 | Zbl

[4] G.S. Akopyan, R.L. Shakhbagyan, “Smeshannaya kraevaya zadacha dlya vyrozhdayuschikhsya nelineinykh uravnenii tipa Soboleva vysokogo poryadka”, Izv. NAN Armenii. Matematika, 30:1 (1995), 17–32 | MR | Zbl

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

[6] A. A. Mamikonyan, “Nachalno-kraevaya zadacha dlya odnogo klassa nelineinykh uravnenii tipa Soboleva”, Uch. zapiski EGU, ser. Fizika i Matematika, 2006, no. 2, 33–40 | Zbl