Solution of nonlinear parabolic equations by finite difference method for an arbitrary time interval
The problem of a solving a class of hypersingular integral equations over the boundary of a nonplanar disc is considered. The solution is obtained by an expansion in basis functions that are orthogonal over the unit disc. A Fourier series in the azimuthal angle, with the Fourier coefficients expanded in terms of Gegenbauer polynomials is employed. These integral equations appear in the study of the interaction of water waves with submerged thin plates.
The author obtains the classification of all invariant Einstein metrics on the following homogeneous spaces: , , , . Combining this with the results of other authors, the classification of all invariant Einstein metrics on all compact simply connected homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature is obtained.