An approximate solution by the Galerkin method of a quasilinear equation with a boundary condition containing the time derivative of the unknown function
Alisher Mamatov)National University of Uzbekistan, Tashkent 100174, UzbekistanSayfiddin Bakhramov)National University of Uzbekistan, Tashkent 100174, UzbekistanAlibek Narmamatov)National University of Uzbekistan, Tashkent 100174, Uzbekistan
ABI
Abstract
In the paper, we consider one boundary value problem of parabolic type with a divergent principal part when the boundary condition contains the time derivative of the unknown function with the dimension of the domain m ≥ 3. An approximate solution of the considered problem is constructed by the Galerkin method. The existence and uniqueness of a generalized solution of the problem is proved in the space H˜1,1(QT).