An initial value method for an inverse problem in wave propagation

1974 ◽  
Vol 15 (3) ◽  
pp. 289-290
Author(s):  
R. Kalaba ◽  
E. Zagustin
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Initial Value

scholarly journals Reconstruction of Initial Wave Field of a Nonsteady-State Wave Propagation from Limited Measurements at a Specific Spatial Point Based on Stochastic Inversion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. L. Han ◽  
Takeshi Kinoshita
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Wave Field ◽  
Simulated Data ◽  
Initial Surface ◽  
Reconstruction Procedure ◽  
Inference Problem ◽  
State Wave ◽  
Initial Wave ◽  
Nonsteady State

This paper studies an inverse problem that can be used for reconstructing initial wave field of a nonsteady-state wave propagation. The inverse problem is ill posed in the sense that small changes in the input data can greatly affect the solution of the problem. To address the difficulty, the problem is formulated in the form of an inference problem in an appropriately constructed stochastic model. It is shown that the stochastic inverse model enables the initial surface disturbance to be reconstructed, including its confidence intervals given the noisy measurements. The reconstruction procedure is illustrated through applications to some simulated data for two- and three-dimensional problem.

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

An initial value problem in the theory of nonlinear wave propagation

1980 ◽  
Vol 4 (4) ◽  
pp. 781-789
Author(s):  
M.N. Oğuztörel[doti] ◽  
E.S. Şuhubi ◽  
M. Teymur
Keyword(s):  
Wave Propagation ◽  
Nonlinear Wave ◽  
Initial Value Problem ◽  
Nonlinear Wave Propagation ◽  
Initial Value

Dynamic Instability in Ice-Lifting From a Flat Road Surface Through Penetration With a Sharp Blade

1982 ◽  
Vol 49 (1) ◽  
pp. 187-190 ◽  
Author(s):  
N. C. Huang
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Initial Value Problem ◽  
Initial Velocity ◽  
Flat Surface ◽  
Dynamic Instability ◽  
Inertia Force ◽  
Initial Value ◽  
Impulsive Load ◽  
Horizontal Thrust

This paper is concerned with the problem of dynamic instability during ice-lifting from a flat surface through penetration of the interface by means of a sharp blade. The blade is subjected to a horizontal impulsive load and a constant horizontal thrust, both applied suddenly and simultaneously. The principle of the balance of energy is used to analyze the deformation of the ice associated with the crack propagation along the interface. In our formulation, the effect of wave propagation in the ice is neglected. However, the inertia force due to the acceleration of the blade is included. The motion of the blade is investigated by the numerical solution of a complex, nonlinear, initial value problem. It is found that under a given horizontal thrust, if the initial velocity of the blade is sufficiently small, the motion of the blade may stop. However, if the initial velocity of the blade is sufficiently large, the motion of the blade is always forward and the crack can propagate indefinitely along the interface.

Inverse problem of wave propagation in a random medium

1982 ◽  
Vol 19 (4) ◽  
pp. 1329-1334
Author(s):  
A. S. Blagoveshchenskii
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Random Medium
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