Inverse problem for a class of one-dimensional wave equations with piecewise constant coefficients

1993 ◽  
Vol 76 (1) ◽  
pp. 13-32 ◽  
Author(s):  
A. Bartoloni ◽  
C. Lodovici ◽  
F. Zirilli
Keyword(s):  
Inverse Problem ◽  
Wave Equations ◽  
Piecewise Constant ◽  
One Dimensional ◽  
Constant Coefficients ◽  
Dimensional Wave

On the metric perturbations of the Reissner–Nordström black hole

1979 ◽  
Vol 367 (1728) ◽  
pp. 1-14 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equations ◽  
Schwarzschild Black Hole ◽  
One Dimensional ◽  
Dimensional Wave

The two pairs of one-dimensional wave equations which govern the odd and the even-parity perturbations of the Reissner–Nordström black hole are derived directly from a treatment of its metric perturbations. The treatment closely parallels the corresponding treatment in the context of the Schwarzschild black hole.

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.

On the Derivatives of the Solutions of One-Dimensional Wave Equations

1950 ◽  
Vol 72 (1) ◽  
pp. 148 ◽  
Author(s):  
Philip Hartman ◽  
Aurel Wintner
Keyword(s):  
Wave Equations ◽  
One Dimensional ◽  
Derivatives Of ◽  
Dimensional Wave

scholarly journals Robustness of Polynomial Stability of Damped Wave Equations

2022 ◽  
Author(s):  
Dmytro Baidiuk ◽  
Lassi Paunonen
Keyword(s):  
Boundary Condition ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Acoustic Boundary Condition ◽  
The Stability ◽  
Perturbed Equation ◽  
Dimensional Wave

AbstractIn this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation with an acoustic boundary condition. In the case of Webster’s equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.

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