функция Бесселя

Nonlocal Boundary-Value Problems in the Cylindrical Domain for the Multidimensional Laplace Equation

Authors: Aldashev S. A.

Correct statements of boundary value problems on the plane for elliptic equations by the method of analytic function theory of a complex variable. Investigating similar questions, when the number of independent variablesis greater than two, problems of a fundamental nature arise. Avery attractive and convenient method of singular integral equations loses its validity due to the absence of any complete theory of multidimensional singular integral equations. The author has previously studied local boundary value problems in a cylindrical domain for multidimensional elliptic equations.

Well-posedness of the Dirichlet Problem for One Class of Degenerate Multi-dimensional Hyperbolic-parabolic Equations

Authors: Aldashev S. A.

It has been shown by Hadamard that one of the fundamental problems of mathematical physics, the analysis of the behavior of oscillating string is an ill-posed problem when the boundary-value conditions are imposed on the entire boudary of the domain. As noted by A. V. Bitsadze and A. M. Nakhushev, the Dirichlet problem is ill-posed not only for the wave equation but for hyperbolic PDEs in general.

Well-posedness of the Dirichlet Problem for a Class of Multidimensional Elliptic-parabolic Equations

Authors: Aldashev S. A.

Correctness of boundary problems in the plane for elliptic equations is well analyzed by analitic function theory of complex variable. There appear principal difficulties in similar problems when the number of independent variables is more than two. An attractive and suitable method of singular integral equations is less strong because of lock of any complete theory of multidimensional singular integral equations.

Correctness of the Local Boundary Value Problem in a Cylindrical Domain for Laplace’s Many-dimensional Equation

Authors: Aldashev S. A.

Correctness of boundary problems in the plane for elliptic equations is well analyzed by analitic function theory of complex variable.
There appear principal difficulties in similar problems when the number of independent variables is more than two. An attractive and suitable method of singular integral equations is less strong because of lock of any complete theory of multidimensional singular integral equations.