ON SOLVABILITY OF THE IDENTIFICATION- INVERSE PROBLEM FOR OPERATOR-FUNCTIONS OF A NONLINEAR REGULATOR OF A NONSTATIONARY HYPERBOLIC SYSTEM

2016 ◽  
Vol 16 (2) ◽  
pp. 71-84 ◽  
Author(s):  
V. A. Rusanov ◽  
A. V. Daneev ◽  
A. V. Lakeev ◽  
Yu. É. Linke
Keyword(s):  
Inverse Problem ◽  
Hyperbolic System ◽  
Operator Functions ◽  
Nonlinear Regulator

scholarly journals An inverse problem for a hyperbolic system on a vector bundle and energy measurements

2011 ◽  
Vol 354 (4) ◽  
pp. 1431-1464
Author(s):  
Katsiaryna Krupchyk ◽  
Matti Lassas
Keyword(s):  
Inverse Problem ◽  
Vector Bundle ◽  
Hyperbolic System

scholarly journals Recovering Density and Speed of Sound Coefficients in the 2D Hyperbolic System of Acoustic Equations of the First Order by a Finite Number of Observations

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 199
Author(s):  
Dmitriy Klyuchinskiy ◽  
Nikita Novikov ◽  
Maxim Shishlenin
Keyword(s):  
Inverse Problem ◽  
Finite Number ◽  
Hyperbolic System ◽  
Speed Of Sound ◽  
Acoustic Waves ◽  
Coefficient Inverse Problem ◽  
Optimization Scheme ◽  
First Order ◽  
Acoustic Equations ◽  
Gradient Based

We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.

Inverse Problem for a First-Order Hyperbolic System with Memory

2020 ◽  
Vol 56 (12) ◽  
pp. 1634-1643
Author(s):  
D. K. Durdiev ◽  
Kh. Kh. Turdiev
Keyword(s):  
Inverse Problem ◽  
Hyperbolic System ◽  
First Order ◽  
With Memory
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