Obidjon Zikirov

National University of Uzbekistan · Faculty of Mathematics

In this paper, we examine the solvability of a mixed problem with an integral condition for a third-order equation whose principal part contains the wave operator. The existence and uniqueness of a classical solution to this problem are proved by the Riemann method.

We consider Dirichlet problem for third-order linear hyperbolic equations. We prove the existence and uniqueness of classical solution by means of an energy inequality and Riemann’s method. We reveal the influence of coefficients at lower derivatives on the well-posedness of the Dirichlet problem.

In the present paper we study some boundary-value problems for a class of third-order composite type equations with Chapligin operator in the main part. We prove the theorems of the existence and uniqueness of classical solution for considered problems. The proof is based on an energy inequality and Fredgolm type integral equations.

This paper studies the problems of existence of classical solutions to the Goursat and Dirichlet problems and also to some nonlocal boundary-value problems for a linear third-order hyperbolic equation in a rectangular domain. The problems studied are reduced to a uniquely solvable integral equation. Thus, theorems of existence, uniqueness, and stab...

In the paper, we study boundary-value problems with the normal derivative for a class of third-order composite type equation with Laplace operator in the main part. We prove the theorems of the existence and uniqueness of classical solution for considered problems. The proof is based on an energy inequality and Fredholm type integral equations.

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Inf...

We consider a Dirichlet problem for the third-order hyperbolic equation and show the existence and uniqueness of its classical solution. For the proof of unique solvability, we use the methods of Riemann’s function and integral equations. Keywordswave operator-boundary-value problem-Dirichlet problem-Goursat problem-Riemann’s function-third-order...

In the paper non‐local boundary value problems for a one class of composite type equation with Laplace operator in the main part has been investigated. Using the methods of energy integrals and integral equations, theorems of the uniqueness and existence of a classical solution were proved. First published online: 14 Oct 2010

We study the problem of the unique solvability of Goursat and Dirichlet problems for one partial differential equation of the third order. We construct a Riemann function for a linear third-order equation with a hyperbolic operator in the principal part, study some properties of the Riemann function, and then use them to prove theorems on the exist...

We consider a non-local boundary value problem for the linear third order equation with hyperbolic operator in the main part. Sufficient conditions were stated to coefficients of the equation and to given functions in order that this non-local boundary value problem has a unique solution. For the proof, we use the Riemann's method.

We formulate some boundary-value problems for a linear third-order equation with hyperbolic operator in the main part and study the unique solvability. Under certain conditions to given functions, using the Riemann method, we obtain an integral representation of solutions.