2019
Том 71
№ 9

All Issues

Aldashev S. A.

Articles: 15
Brief Communications (English)

Well-posedness of the Dirichlet problem in a cylindrical domain for three-dimensional elliptic equations with degeneration of type and order

Aldashev S. A., Kitaibekov E. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1270-1274

The paper shows the unique solvability of the classical Dirichlet problem in cylindrical domain for three-dimensional elliptic equations with degeneration type and order.

Brief Communications (Russian)

Well-posedness of mixed problems for multidimensional hyperbolic equations with wave operator

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 992-999

We establish the unique solvability and obtain the explicit expression for the classical solution of the mixed problem for multidimensional hyperbolic equations with wave operator.

Brief Communications (Russian)

Well-Posedness of the Dirichlet and Poincaré Problems for the Wave Equation in a Many-Dimensional Domain

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1414–1419

We determine a many-dimensional domain in which the Dirichlet and Poincaré problems for the wave equation are uniquely solvable.

Brief Communications (Russian)

Well-posedness of the Dirichlet and Poincare problems for a multidimensional Gellerstedt equation in a cylindric domain

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 426-432

We prove the unique solvability of the Dirichlet and Poincare problems for a multidimensional Gellerstedt equation in a ´cylindric domain. We also obtain a criterion for the unique solvability of these problems.

Brief Communications (Russian)

Eigenvalues and eigenfunctions of the Gellerstedt problem for the multidimensional Lavrent?ev?Bitsadze equation

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 6. - pp. 827-832

Eigenvalues and eigenfunctions of the Hellerstedt problems for the Lavrentiev - Bitsadze multidimensional equation are found.

Article (Russian)

Existence of eigenfunctions of the Tricomi spectral problem for some classes of multidimensional mixed hyperbolic–parabolic equations

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 723 – 732

We show that there exists a countable set of eigenfunctions of the Tricomi spectral problem for multidimensional mixed hyperbolic–parabolic equations.

Brief Communications (Russian)

Nonuniqueness of the solution of the gellerstedt space problem for one class of many-dimensional hyperbolic-elliptic equations

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 265–269

It is shown that the solution of the Gellerstedt space problem is not unique for one class of multidimensional hyperbolic-elliptic equations.

Brief Communications (Russian)

Criterion for the uniqueness of a solution of the Darboux-Protter problem for multidimensional Hyperbolic equations with Chaplygin operator

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1119–1127

We obtain a criterion for the uniqueness of a regular solution of the Darboux-Protter problem for multidimensional hyperbolic equations with Chaplygin operator. We also prove a theorem on the uniqueness of solutions of the dual problem.

Article (Russian)

Criterion for the Uniqueness of a Solution of the Darboux–Protter Problem for Degenerate Multidimensional Hyperbolic Equations

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 11. - pp. 1569-1575

We obtain a criterion for the uniqueness of a regular solution of the Darboux–Protter problem for degenerate multidimensional hyperbolic equations.

Brief Communications (Russian)

Darboux–Protter Spectral Problems for One Class of Multidimensional Hyperbolic Equations

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 1. - pp. 100-107

For a multidimensional hyperbolic equation with a wave operator in the principal part, we show that the Darboux–Protter spectral problem has the countable set of eigenfunctions, and its dual problem is the Volterra problem.

Article (Russian)

Some problems for multidimensional integro-differential equations of hyperbolic type

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 5. - pp. 590-595

We prove the well-posedness of the Cauchy, Goursat, and Darboux problems for multidimensional in-tegro-differential equations of the hyperbolic type encountered in biology.

Article (Russian)

Many-dimensional Dirichlet and Tricomi problems for one class of hyperbolic-elliptic equations

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1587–1593

For the generalized many-dimensional Lavrent’ev-Bitsadze equation, we prove the unique solvability of the Dirichlet and Tricomi problems. We also establish the existence and uniqueness of a solution of the Dirichlet problem in the hyperbolic part of a mixed domain.

Brief Communications (Russian)

On the well-posedness of derichlet problems for the many-dimensional wave equation and lavrent’ev-bitsadze equation

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 702-706

We prove the unique solvability of the Dirichlet problems for the many-dimensional wave equation and Lavrent’ev-Bitsadze equation.

Article (Russian)

Well-posedness of many-dimensional Darboux problems for degenerating hyperbolic equations

Aldashev S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1304–1311

Forthe equation $$\sum^{m}_{i=t}t^{k_i}U_{x_i,x_i} - U_n + \sum^{m}_{i=t} a_i(x,t)U_{x_i} + b(x, t)u_t + c(x,t)u = 0,$$ $$k_i = \text{const} ≥ 0,\; i = l ..... m, x = (x_1,..., x_m),\; m_>2,$$ we find a many-dimensional analog of the well-known "Gellerstedt condition" $$ a_i(x,t) = O(1)t^{\alpha},\; i = 1,..., m,\, \alpha >\frac{k_1}{2} - 2.$$ We prove that if this condition is satisfied, then the Darboux problems are uniquely solvable.

Article (Ukrainian)

Some boundary-value problems for linear multidimensional second-order hyperbolic equations

Aldashev S. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 415-420