The Impedance Boundary Value Problem for the Helmholtz Equation in a Half-Plane

1997 ◽  
Vol 20 (10) ◽  
pp. 813-840 ◽  
Author(s):  
S. N. Chandler-Wilde
Keyword(s):  
Boundary Value Problem ◽  
Helmholtz Equation ◽  
Half Plane ◽  
Boundary Value ◽  
Impedance Boundary

scholarly journals On the approximate solution of the boundary value problem for the Helmholtz equation with impedance condition

2019 ◽  
Vol 488 (3) ◽  
pp. 233-236
Author(s):  
A. R. Aliev ◽  
R. J. Heydarov
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Boundary Value Problem ◽  
Error Estimate ◽  
Helmholtz Equation ◽  
Collocation Method ◽  
Boundary Value ◽  
Impedance Boundary ◽  
Impedance Condition

In this work, we present a justification of collocation method for integral equation of the impedance boundary value problem for the Helmholtz equation. We also build a sequence which converges to the exact solution of our problem and we obtain an error estimate.

scholarly journals RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM

2009 ◽  
Vol 06 (03) ◽  
pp. 577-614 ◽  
Author(s):  
GILLES CARBOU ◽  
BERNARD HANOUZET
Keyword(s):  
Boundary Value Problem ◽  
Response Time ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Debye Model ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Initial Boundary Value

The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an instantaneous response of the material, or by the Kerr–Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and two-dimensional transverse electric cases, the global existence of smooth solutions for the Kerr–Debye system is established. When the response time tends to zero, the convergence of the Kerr–Debye model to the Kerr model is established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr–Debye model.

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