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Publications (7)
The Dirichlet problem for sixth order improperly elliptic equation is considered. The functional class of boundary functions, where this problem is normally solvable is determined. If the roots of the characteristic equation satisfy some conditions, the number of linearly independent solutions of homogeneous problem and the number of linearly indep...
The Dirichlet problem for sixth-order improperly elliptic equation is considered. The functional class of boundary functions, where this problem is normally solvable is determined. If the roots of the characteristic equation satisfy some conditions, the number of linearly independent solutions of the homogeneous problem and the number of linearly i...
In this paper we present the numerical method for the solution of the Riemann problem for the second-order improperly elliptic equation. First, we reduce this problem to boundary value problems for properly elliptic equations, and after that we solve these problems by the grid method.
MSC:
35G45, 35G15, 35J25, 35J57, 65N06, 65N20.
The paper studies boundary value problems for some systems of nonlinear ordinary differential equations, that have important applications. The existence of a solution in a finite interval with starting point fixed, whose endpoint has to be determined from the boundary conditions is proved, and estimates that allow a construction of approximate solu...
The paper considers a Dirichlet-type boundary value problem for the elliptic equation ∂ m+n u ∂z ¯ m ∂z n =0,∂u ∂z ¯≡1 2∂u ∂x+i∂u ∂y,∂u ∂z≡1 2∂u ∂x-i∂u ∂y in a multiply connected domain. The problem is reduced to a Dirichlet problem for the n-harmonic equation. An existence theorem is proved.
