No. 37 (254), issue 10Pages 22 - 29

THE INITIAL-FINISH VALUE PROBLEM FOR NONHOMOGENIOUS BOUSSINESQUE - L'OVE EQUATION

A.A. Zamyshlyaeva
We investigate the initial-finish value problem for the Boussinesque-L'ove equation by reducing it to the initial-finish value problem for the Sobolev type equation of the second order. We obtain sufficient conditions about the unique solvability of original and abstract problems.
Full text
Keywords
the Sobolev type equations, the M,N-functions, the initial-finish value problem.
References
1. Uizem J. Lineynye i nelineynye volny [Linear and nonlinear waves]. Moscow, Mir, 1977.
2. Sviridyuk G.A., Fedorov V.E. Linear Sobolev type equations and degenerate semigroups of operators. Utrecht, Boston, K'oln, Tokyo: VSP, 2003.
3. Zagrebina S.A. On Showalter - Sidorov problem [O zadache Shouoltera - Sidorova] Izvestiya vuzov. Matematika, 2007, no. 3, pp. 22 - 28.
4. Manakova N.A., Dylkov A.G.Optimal control of solutions of initial-finish problem for the linear Sobolev type equations [Optimal'noe upravlenie resheniyami nachal'no-konechnoy zadachi dlya lineynykh uravneniy sobolevskogo tipa] Vestnik Yuzhno-Ural'skogo gosudarstvennogo universiteta. Seriya "Matematicheskoe modelirovanie i programmirovanie", 2011, no. 17 (234), vyp. 8, pp. 113 - 114.
5. Zamyshlyaeva A.A. The phase spaces of a class of linear sobolev type equations of the second order [Fazovye prostranstva odnogo klassa lineynykh uravneniy sobolevskogo tipa]. Vychislitel'nye tekhnologii, 2003, vol. 8, no. 4, pp.45 - 54.