An existence theorem for an inverse problem for a semilinear hyperbolic system

2004 ◽  
Vol 40 (9) ◽  
pp. 1221-1232 ◽  
Author(s):  
A. M. Denisov
Keyword(s):  
Inverse Problem ◽  
Existence Theorem ◽  
Hyperbolic System

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 On a hyperbolic system arising in liquid crystals modeling

2018 ◽  
Vol 15 (01) ◽  
pp. 15-35 ◽  
Author(s):  
Eduard Feireisl ◽  
Elisabetta Rocca ◽  
Giulio Schimperna ◽  
Arghir Zarnescu
Keyword(s):  
Liquid Crystals ◽  
Initial Data ◽  
Existence Theorem ◽  
Hyperbolic System ◽  
Finite Energy ◽  
Classical Solutions ◽  
System Of Differential Equations ◽  
Dissipative Solutions ◽  
Nonlinear Hyperbolic System ◽  
Time Existence

We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution is proposed, for which a global-in-time existence theorem is shown. The dissipative solutions enjoy the following properties: (i) they exist globally in time for any finite energy initial data; (ii) dissipative solutions enjoying certain smoothness are classical solutions; (iii) a dissipative solution coincides with a strong solution originating from the same initial data as long as the latter exists.

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.

On the Hochstadt–Lieberman type problem with eigenparameter dependent boundary condition

2020 ◽  
Vol 28 (4) ◽  
pp. 557-565
Author(s):  
Sheng-Yu Guan ◽  
Chuan-Fu Yang ◽  
Natalia Bondarenko ◽  
Xiao-Chuan Xu ◽  
Yi-Teng Hu
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Existence Theorem ◽  
Liouville Operator ◽  
Entire Functions ◽  
Finite Interval ◽  
Type Problem ◽  
Reconstruction Procedure ◽  
Half Inverse Problem ◽  
Sturm Liouville

AbstractThe half-inverse problem is studied for the Sturm–Liouville operator with an eigenparameter dependent boundary condition on a finite interval. We develop a reconstruction procedure and prove the existence theorem for solution of the inverse problem. Our method is based on interpolation of entire functions.

Sign in / Sign up

Export Citation Format

Share Document