The Inverse Problem for the Wave Equation with an Unknown Source

1971 ◽  
pp. 23-33
Author(s):  
A. S. Blagoveshchenskii
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Unknown Source

An Inverse Problem for an Unknown Source Term in a Wave Equation

1983 ◽  
Vol 43 (3) ◽  
pp. 553-564 ◽  
Author(s):  
J. R. Cannon ◽  
P. DuChateau
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Source Term ◽  
Unknown Source

A method of linearizing the inverse problem for the wave equation

1987 ◽  
Vol 27 (5) ◽  
pp. 157-165
Author(s):  
I.P. Borovikov ◽  
Yu.L. Gaponenko
Keyword(s):  
Inverse Problem ◽  
Wave Equation

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

scholarly journals Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation

2019 ◽  
Vol 13 (3) ◽  
pp. 575-596 ◽  
Author(s):  
Jussi Korpela ◽  
◽  
Matti Lassas ◽  
Lauri Oksanen ◽  
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Dimensional Wave

Inverse problem for one-dimensional wave equation with matrix potential

2019 ◽  
Vol 27 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Ammar Khanfer ◽  
Alexander Bukhgeim
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Uniqueness Theorem ◽  
Cauchy Data ◽  
Global Uniqueness ◽  
One Dimensional ◽  
Matrix Potential ◽  
The Matrix ◽  
Real Matrices ◽  
Dimensional Wave

AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0}, {x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix {\partial_{t}a} is known.

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.

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