scholarly journals Finding scattering data for a time-harmonic wave equation with first order perturbation from the Dirichlet-to-Neumann map

2015 ◽  
Vol 23 (6) ◽  
Author(s):  
Alexey D. Agaltsov
Keyword(s):  
Wave Equation ◽  
Harmonic Wave ◽  
Order Perturbation ◽  
Scattering Data ◽  
Scalar Case ◽  
First Order ◽  
Time Harmonic ◽  
General Scalar ◽  
Dirichlet To Neumann Map ◽  
First Order Perturbation

AbstractWe present formulas and equations for finding scattering data from the Dirichlet-to-Neumann map for a time-harmonic wave equation with first order perturbation with compactly supported coefficients. We assume that the coefficients are matrix-valued in general. To our knowledge, these results are new even for the general scalar case.

scholarly journals An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator

2021 ◽  
Author(s):  
Sombuddha Bhattacharyya ◽  
Tuhin Ghosh
Keyword(s):  
Inverse Problem ◽  
Vector Field ◽  
Symmetric Matrix ◽  
Symmetric Tensor ◽  
Second Order ◽  
Order Perturbation ◽  
Biharmonic Operator ◽  
First Order ◽  
Dirichlet To Neumann Map ◽  
First Order Perturbation

AbstractThis article offers a study of the Calderón type inverse problem of determining up to second order coefficients of higher order elliptic operators. Here we show that it is possible to determine an anisotropic second order perturbation given by a symmetric matrix, along with a first order perturbation given by a vector field and a zero-th order potential function inside a bounded domain, by measuring the Dirichlet to Neumann map of the perturbed biharmonic operator on the boundary of that domain.

Note on Interference Effects in Two-Step Reaction Processes

1975 ◽  
Vol 53 (23) ◽  
pp. 2590-2592
Author(s):  
J. Cejpek ◽  
J. Dobeš
Keyword(s):  
Perturbation Theory ◽  
Point Of View ◽  
Order Perturbation ◽  
Interference Effects ◽  
Qualitative Explanation ◽  
First Order ◽  
One Step ◽  
Step Transition ◽  
Reaction Processes ◽  
First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

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