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## Publications

Publications (20)

The goal of this project is the development of a Simplified Simulator for Student Training for one of the nuclear power plant's main equipment, namely the steam generator. The TRIPLE S simulator is designed for basic understanding of undergraduate students in nuclear engineering educational programs. Scilab is used to implement a simulation model a...

In the present paper we study a Darboux-Goursat problem for a hyperbolic equation with a singular coefficient, where a third-type boundary condition on the non-characteristic segment is imposed. This problem is related to a four-dimensional Protter's problem for the wave equation and it has an unique generalized solution with possible singularity a...

The Protter’s problems are multidimensional variants of the 2-D Darboux problems for hyperbolic and weakly hyperbolic equations and they are not well-posed in the frame of classical solvability, since their adjoint homogeneous problems have infinitely many nontrivial classical solutions. The generalized solutions of the Protter’s problem may have s...

Here we present our handy and convenient program for numerical solving of various heat transfer problems in 2-D regions composed of different material blocks. This application is based on Scilab.

We study a boundary value problem for a multidimensional weakly hyperbolic Keldysh-type equation (Problem PK). This problem is analogous to a similar one proposed by M. Protter in 1952, but for Tricomi-type equations known with their applications in transonic fluid dynamics. For their part, the Keldysh-type equations are known in some specific appl...

In series of our works ([6, 7, 18, 19]) we considered a four-dimensional Protter-Morawetz problem for a Keldysh-type weakly hyperbolic equation with power-type degeneracy of order m, where 0 < m < 2. It was shown that this problem is not well posed, since it has an infinite-dimensional cokernel, but it can be studied in the frame of generalized sol...

In this work a Darboux-Goursat problem for a hyperbolic equation with a singular coefficient is considered. Such a problem arises in the study of multidimensional boundary value problems which are not well-posed. Here the well known results concerning the exact behavior of a generalized solution with possible big singularity are made more precise.

We study a boundary value problem for (3 + 1)-D weakly hyperbolic equations of Keldysh type (problem PK). The Keldysh-type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this problem is analogous to a s...

A (3 + 1)-dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems for equations of Tricomi type (the first kind) or for the wave equation were formulated by M.H. Protter (1954) as multidimensional analogues of Darboux or Cauchy-Goursat plane problems. Now, it is well known that Protter problems a...

A (3 + 1)-dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems for equations of Tricomi type (the first kind) or for the wave equation were formulated by M.H. Protter (1954) as multidimensional analogues of Darboux or Cauchy-Goursat plane problems. Now, it is well known that Protter problems a...

http://www.proceedings.bas.bg/cgi-bin/mitko/0DOC_abs.pl?2017_2_02

This paper deals with Protter problems for Keldysh type equations in ℝ4. Originally such type problems are formulated by M. Protter for equations of Tricomi type. Now it is well known that Protter problems for mixed type equations of the first kind are ill-posed and for smooth right-hand side functions they have singular generalized solutions. In t...

We consider a (2+1)-D boundary value problem for degenerate hyperbolic equation, which is closely connected with transonic fluid dynamics. This problem was introduced by Protter in 1954 as a multi-dimensional analogue of the Darboux problem in the plain, which is known to be well-posed. However the (2+1)-D problem is overdetermined with infinitely...

We consider the Protter problem for the four-dimensional wave equation, where the boundary conditions are posed on a characteristic surface and on a non-characteristic one. In particular, we consider a case when the right-hand side of the equation is of the form of harmonic polynomial. This problem is known to be ill-posed, because its adjoint homo...

We consider a planar Darboux-Goursat problem with singular coefficients. It is known that its unique solution (which is not a solution in the classical sense) may have strong power type singularity isolated at one boundary point even for very smooth functions in the right-hand side of the equation. In the present work we derive an exact asymptotic...

We consider some boundary value problems for a weakly hyperbolic equation, which are three-dimensional analogues of the Darboux problems on the plain. These problems arise in transonic fluid dynamics and they are introduced by Protter in 1952. As distinct from the planar Darboux problems, the Protter problems are not well posed since the homogeneou...

In 1952 M. H. Protter introduced some boundary value problems for weakly
hyperbolic equations in a domain bounded by two characteristic surfaces
and non-characteristic plane region. Such problems arise in fluid
dynamics. They are multidimensional analogues of the Darboux problems on
the plain. The Protter problems are not well possed since the
homo...

For the (2+1)-D wave equation Protter formulated (1952) some boundary value problems which are three-dimensional analogues of the Dar-boux problems on the plane. Protter studied these problems in a 3-D domain, bounded by two characteristic cones and by a planar region. Now it is well known that, for an infinite number of smooth functions in the rig...