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卷 237, 编号 4 (2019)
- 年: 2019
- 文章: 10
- URL: https://ogarev-online.ru/1072-3374/issue/view/14990
Article
Operator Formulas in Inverse Problems for Evolution Equations
摘要
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
The Asymptotic Behavior of the Mean Sojourn Time for a Random Walk Above a Receding Curvilinear Boundary
摘要
We study the asymptotic behavior of the mean sojourn time for a random walk above a receding curved boundary in the case where the jump distribution satisfies the Cramèr condition.
511-520
Optimal Control by the Rigid Layer Size of a Construction
摘要
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
摘要
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
The Bitsadze Problem for a Multidimensional Hyperbolic Equation
摘要
We prove the unique solvability of the Bitsadze problem for multidimensional hyperbolic equation.
546-548
Nonlocal Boundary Value Problems with Partially Integral Conditions for Degenerate Differential Equations with Multiple Characteristics
摘要
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
Nonuniqueness of the Solution to the Interior Neumann–Gellerstedt Problem for the Lavrent’ev–Bitsadze Equation
摘要
We prove that the homogeneous Neumann–Gellerstedt problem with data on internal characteristics has a nontrivial solution under the Frankl matching condition on the line where the equation changes type.
563-568
Generalized Functional Invariant Solutions of the Wave Equation in Dimension 2
摘要
We describe generalized functional invariant solutions to the wave equation in dimension 2 for phase functions of travelling wave type.
569-575
Inverse Source and Coefficient Problems for Elliptic and Parabolic Equations in Hölder and Sobolev Spaces
摘要
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
摘要
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