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Том 236, № 1 (2019)
- Год: 2019
- Статей: 7
- URL: https://ogarev-online.ru/1072-3374/issue/view/14977
Article
On the Development of Investigations of the Thermomechanical Behavior of Thermally Sensitive Bodies
Аннотация
We present a brief analysis of the investigations carried out in the mechanics of coupled fields with regard for the thermomechanical behavior of thermally sensitive bodies carried out by the researchers of the Lviv scientific school in recent years.
1-20
Direct and Inverse Problems of Thermomechanics Concerning the Optimization and Identification of the Thermal Stressed State of Deformed Solids
Аннотация
We describe the main stages of the development of investigations originated by Prof. Vihak in the fields of the theory and methods of optimal control over the thermal processes and thermal stressed state of deformed solids, theory of inverse problems of heat conduction and thermomechanics, and the mathematical methods in the mechanics of deformable solids. We indicate the existence of close relationship between the obtained theoretical results and the applied problems of thermal power engineering motivating investigations of this kind. We describe a significant contribution made by the researchers of the Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of the Ukrainian National Academy of Sciences to the development of investigations in these fields. The prospects of further development of these studies are analyzed and some facts from the life and creative activity of Prof. V. М. Vihak are presented.
21-34
On the Kernel of a Two-Point Problem for a Partial Differential Equation of the Second Order in Time
Аннотация
We study the problem for a homogeneous partial differential equation of the second order with respect to time with given homogeneous two-point conditions in this variable and, in general, of the infinite order in the other (space) variable. It is proved that the analyzed problem possesses solely the trivial solution if the characteristic determinant is not identically equal to zero. In the case where the set of zeros of the characteristic determinant of this problem is nonempty, we propose a method for the construction of nontrivial solutions of the problem.
35-52
Boundary-Value Problems with Impulsive Conditions for Parabolic Equations with Degenerations
Аннотация
We consider the first boundary-value problem and the unilateral boundary-value problem with impulsive conditions with respect to the time variable for a linear parabolic equation with power singularities of any order in the space variables. With the help of the maximum principle and a priori estimates, we establish the existence and uniqueness of the solutions of the posed problems in the Hölder spaces with power weights.
53-70
Structure of Rank-One Matrices Over the Domain of Principal Ideals Relative to Similarity Transformations
Аннотация
We study the structure of rank-one matrices over the domain of principal ideals relative to equivalence and similarity transformations. The canonical form of rank-one matrices relative to similarity transformations is established. We propose conditions under which a pair of rank-one matrices is reduced to the triangular form by a similarity transformation.
71-82
Geometric Aspects of Analytic Functions
Аннотация
We study a pair of surfaces associated with a function analytic in a domain G, establish relations between the coefficients of the first (second) fundamental quadratic forms of these surfaces and prove theorems on their invariance under conformal transformations.
83-97
Combination of the Laguerre Transform with the Boundary-element Method for the Solution of Integral Equations with Retarded Kernel
Аннотация
We apply the Laguerre transform with respect to time to a time-dependent boundary-value integral equation encountered in the solution of three-dimensional Dirichlet initial-boundary-value problems for the homogeneous wave equation with homogeneous initial conditions by using the retarded potential of single layer. The obtained system of boundary integral equations is reduced to a sequence of Fredholm integral equations of the first kind that differ solely by the recursively dependent right-hand sides. To find their numerical solution, we use the boundary-element method. We establish an asymptotic estimate of the error of numerical solution and present the results of numerical simulations aimed at finding the solutions of retarded-potential integral equations for model examples.
98-114