scholarly journals A limiting absorption principle for the Helmholtz equation with variable coefficients

2018 ◽  
Vol 8 (4) ◽  
pp. 1349-1392 ◽  
Author(s):  
Federico Cacciafesta ◽  
Piero D'Ancona ◽  
Renato Lucà
Keyword(s):  
Helmholtz Equation ◽  
Variable Coefficients ◽  
Limiting Absorption Principle

The BEM for solving the nonhomogeneous Helmholtz equation with variable coefficients

1996 ◽  
Vol 17 (1) ◽  
pp. 85-89 ◽  
Author(s):  
Wang Shouxin ◽  
Liu Xiping ◽  
Peng Tianguo ◽  
Zhao Zhongsheng ◽  
Zhao Suhua
Keyword(s):  
Helmholtz Equation ◽  
Variable Coefficients

scholarly journals A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains

2013 ◽  
Vol 143 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Juan Antonio Barceló ◽  
Luca Fanelli ◽  
Alberto Ruiz ◽  
Maricruz Vilela
Keyword(s):  
Helmholtz Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Exterior Domains ◽  
Limiting Absorption Principle ◽  
Electromagnetic Potentials ◽  
Priori Estimates ◽  
Embedded Eigenvalues

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension n ≥ 3. Using multiplier techniques in the style of Morawetz, we prove a family of a priori estimates from which the limiting absorption principle follows. Moreover, we give some standard applications to cases with an absence of embedded eigenvalues and zero resonances, under explicit conditions on the potentials.

scholarly journals Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

2014 ◽  
Vol 144 (4) ◽  
pp. 857-890 ◽  
Author(s):  
Miren Zubeldia
Keyword(s):  
Helmholtz Equation ◽  
Unique Solution ◽  
A Priori ◽  
Radiation Condition ◽  
Singular Potentials ◽  
Absorption Method ◽  
Limiting Absorption Principle ◽  
Electric Potentials ◽  
Image Position

We study the Helmholtz equationin ℝd with magnetic and electric potentials that are singular at the origin and decay at ∞. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.

Scattering of SH waves around circular canyon in inhomogeneous wedge space

2020 ◽  
Vol 223 (1) ◽  
pp. 45-56
Author(s):  
Zailin Yang ◽  
Xinzhu Li ◽  
Yunqiu Song ◽  
Guanxixi Jiang ◽  
Menghan Sun ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Helmholtz Equation ◽  
Ground Motion ◽  
Governing Equation ◽  
Function Method ◽  
Complex Function ◽  
Variable Coefficients ◽  
Sh Waves ◽  
Free Condition ◽  
Complex Function Method

SUMMARY Scattering of SH waves around a circular canyon in radial inhomogeneous wedge space is investigated in this paper. Based on the complex function method, the governing equation with variable coefficients is transformed into a standard Helmholtz equation and the corresponding analytical solution to this problem is derived. The unknown coefficients in the wavefield is obtained by enforcing the stress-free condition in the circular canyon, then the incident, reflected and scattering waves in the total wavefield are all acquired. Through the calculation and analysis of the parameters that affect the ground motion, the influence of the circular canyon on the ground motion in the radial inhomogeneous wedge space is obtained. Moreover, combined with graphical results, the effects by inhomogeneous parameter on ground motion with circular canyon in wedge space are conspicuous.

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