Application of the carleman boundary-value problem to the investigation of wave propagation in a medium with smooth transition

1987 ◽  
Vol 38 (6) ◽  
pp. 671-674
Author(s):  
V. A. Kozlovskii
Keyword(s):  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Smooth Transition ◽  
Carleman Boundary ◽  
Carleman Boundary Value Problem

scholarly journals Inverse boundary-value problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5259-5271
Author(s):  
Elvin Azizbayov ◽  
Yashar Mehraliyev
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Longitudinal Wave ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Boundary Value ◽  
Inverse Boundary ◽  
Longitudinal Wave Propagation

We study the inverse coefficient problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions. The main purpose of this paper is to prove the existence and uniqueness of the classical solutions of an inverse boundary-value problem. To investigate the solvability of the inverse problem, we carried out a transformation from the original problem to some equivalent auxiliary problem with trivial boundary conditions. Applying the Fourier method and contraction mappings principle, the solvability of the appropriate auxiliary inverse problem is proved. Furthermore, using the equivalency, the existence and uniqueness of the classical solution of the original problem are shown.

scholarly journals BEM ANALYSIS OF WAVE PROPAGATION IN POROVISCOELASTIC LAYERED HALFSPACE AND HALFSPACE WITH CAVITY

2020 ◽  
Vol 82 (3) ◽  
pp. 364-376
Author(s):  
A.A. Ipatov
Keyword(s):  
Wave Propagation ◽  
Boundary Value Problem ◽  
Laplace Transform ◽  
Boundary Element ◽  
Half Space ◽  
Viscoelastic Material ◽  
Boundary Value ◽  
Heaviside Function ◽  
Biot Model ◽  
The Laplace Transform

The paper is dedicated to the wave propagation a porous-viscoelastic material. As a mathematical model of a fully saturated poroelastic medium, we consider the Biot model with four basic functions – pore pressure and skeleton movements. The Biot model is supplemented by the principle of elastic and viscoelastic reaction correspondence. The skeleton of a porous material is assumed to be viscoelastic material. A model of a standard viscoelastic solid is spplied to describe the viscoelastic properties of a skeleton. The initial boundary-value problem is reduced to a boundary-value problem by formal application of the Laplace transform. To solve boundary integral equations, the boundary element method is performed. Quadrangular eight-node biquadratic elements are used for boundary element discretization. Numerical integration is carried out according to Gaussian quadrature formulas using algorithms for lowering the order and eliminating features. To obtain a solution in explicit time, numerical inversion of the Laplace transform is applied based on the Durbin algorithm with a variable frequency step. This study is a development of the existing boundary-element technique for solving problems on layered porous-elastic half-spaces. This will allow you to take into account the heterogeneity of the soil in depth. The problem of the action of a vertical force in the form of the Heaviside function on the surface of a layered porous-elastic half-space and a half-space with a cavity is considered. Variants of a homogeneous and heterogeneous half-space are considered. Under the model of heterogeneity we understand the piecewise homogeneous solid. The responses of the boundary displacements on the surface of the half-space are presented. The effect of the viscoelastic material model parameter on the dynamic response of displacements is demonstrated. It is established that the viscosity parameters have a significant effect on the nature of the distribution of parameters of wave processes.

scholarly journals A boundary value problem for cold plasma dynamics

2003 ◽  
Vol 2003 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Thomas H. Otway
Keyword(s):  
Hilbert Space ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Hyperbolic System ◽  
Weak Solutions ◽  
Cold Plasma ◽  
Boundary Value ◽  
Plasma Dynamics

A weak Guderley-Morawetz problem is formulated for a mixed elliptic-hyperbolic system that arises in models of wave propagation in cold plasma. Weak solutions are shown to exist in a weighted Hilbert space. This result extends the work of Yamamoto (1994).

scholarly journals MATHEMATICAL SIMULATION OF THE SYSTEM SEISMIC FLUCTUATIONS, WHICH CONSISTS OF THE TAILINGS DUMP EMBANKMENT DAM, THE MATERIAL OF DEPOSIT (TAILS) AND UNDER BOTTOM GROUND LAYERS

2016 ◽  
Author(s):  
И.Д. Музаев
Keyword(s):  
Mathematical Model ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Seismic Wave Propagation ◽  
Contact Boundary ◽  
Embankment Dam ◽  
Seismic Vibrations ◽  
Contact Surfaces ◽  
The Mathematical Model

Разработана математическая модель совместных сейсмических колебаний системы, состоящей из дамбы обвалования хвостохранилища, материала отложения (хвосты) и подподошвенных слоев грунтового массива. Модель представляет собой контактную краевую задачу для дифференциального уравнения сдвигово-вязких поперечных колебаний тела дамбы с материалами отложений, а также для дифференциальных уравнений сдвигово-вязких поперечных колебаний слоев массива грунта. Эти уравнения взаимосвязаны через граничные условия на контактных поверхностях. Краевая задача решена аналитически. Получены расчетные формулы для вычисления перемещений, скорости и ускорения тела дамбы при распространении падающей на систему сейсмической волны в слоях грунта и в теле дамбы The mathematical model of the system seismic vibrations, which consists of the tailings dump embankment dam, the material of deposit (tails) and under botto ground layers is developed. Model is contact boundary-value problem for the differentialequation of the dam body shift- viscous lateral oscillations with the materials of deposits, and also for the differential equations of the shift- viscous lateraloscillations of the ground layers. These equations are interconnected through the boundary conditions on the contact surfaces. Boundary-value problem is solved analytically. Calculation formulas for enumerating of displacements, velocity and acceleration calculation of the dam body with the seismic wave propagation in the ground layers and into in the dam body.

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