卷 213, 编号 6 (2016)

Propagation of nonlinear waves in a two-layer fluid in the shallow water approximation is considered. In a horizontal channel with a free surface and under lid, the large amplitude subsurface solitary waves describing the wave with “trapped core” are investigated. The flow regime diagram for solitary waves is constructed in the plane of governing parameters. Bibliography: 17 titles. Illustrations: 3 figures.

In a real Banach space, we consider linear bounded invertible operators such that the norms of their powers are nonquasianalytic. We obtain the condition of the existence of a nontrivial invariant subspace and the condition of decomposability (in the sense of Foia¸s) of such operators. Bibliography: 14 titles.

We prove the existence and uniqueness of a solution in the space W₂^2,1(Q) to the first boundary value problem for a semilinear parabolic equation in a cylindrical domain Q ⊆ Rⁿ⁺¹. We obtain an error estimate in the W₂^1,0(Q)-norm in terms of eigenvalues of the selfadjoint spectral problem for a second order elliptic equation. Bibliography: 5 titles.

We consider single-valued meromorphic functions and differentials on finite Riemann surfaces. We construct elementary q-differentials of all types. We find the dimension of two important quotient spaces of Abelian q-differentials, in particular, the first holomorphic de Rham cohomology group of 1-differentials. For these quotient spaces we construct bases that locally holomorphically depend on the moduli of the Riemann surfaces. Bibliography: 6 titles.

We obtain a representation of the solution to the Cauchy problem with a polynomial difference operator. We establish the solvability condition and specify it in the twodimensional case. Bibliography: 9 titles.

We establish the well-posedness of the problem for a degenerate hyperbolic equation of the first kind in the characteristic triangle with integral perturbation in the Cauchy data along the degeneracy line. Bibliography: 16 titles.