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Том 237, № 4 (2019)
- Год: 2019
- Статей: 10
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14990
Article
Operator Formulas in Inverse Problems for Evolution Equations
Аннотация
We present general representations of solutions to the inverse problems for evolution equations and write out the second kind equations related to construction of special solutions to nonlinear equations generated by mappings of the Euclidean spaces.
501-510
511-520
Optimal Control by the Rigid Layer Size of a Construction
Аннотация
We study equilibrium of a two-layer construction of elastic and rigid layers with a crack along the line joining the layers. We consider the limit problem as the rigid layer size tends to zero and the optimal control problem where the cost functional is the derivative of the energy functional with respect to the crack length and the control parameter characterizes the rigid layer size.
521-529
On Contact Between a Thin Obstacle and a Plate Containing a Thin Inclusion
Аннотация
We consider problems governing a contact between an elastic plate with a thin elastic inclusion and a thin elastic obstacle and study the equilibrium of the plate with or without cuts. We discuss various statements and establish the existence of a solution. We analyze the limit problem as the rigidity parameter of the elastic inclusion tends to infinity.
530-545
546-548
Nonlocal Boundary Value Problems with Partially Integral Conditions for Degenerate Differential Equations with Multiple Characteristics
Аннотация
We study the solvability of new local and nonlocal boundary-value problems for degenerate differential equations with multiple characteristics. We establish the existence of regularsolutions and discuss possible generalizations and improvements of the obtained result.
549-562
563-568
569-575
Inverse Source and Coefficient Problems for Elliptic and Parabolic Equations in Hölder and Sobolev Spaces
Аннотация
We review some results obtained by the authors during the last 15 years. In particular, we present the existence and uniqueness theorems for linear and nonlinear inverse problems of reconstructing unknown coefficients in elliptic and parabolic equations.
576-594
Dirichlet Type Problems for First Order Strictly Hyperbolic Systems with Constant Coefficients in a Two-Dimensional Domain
Аннотация
We consider a first order strictly hyperbolic system of four equations with constant coefficients in a bounded domain with piecewise boundary consisting of eight smooth noncharacteristic arcs. In this domain, we consider boundary value problems with two linear relations between components of the solution and show show that these problems are uniquely solvable under certain assumptions.
595-609