scholarly journals Besov estimates in the high-frequency Helmholtz equation, for a non-trapping and C2 potential

2006 ◽  
Vol 228 (2) ◽  
pp. 440-485 ◽  
Author(s):  
François Castella ◽  
Thierry Jecko
Keyword(s):  
Helmholtz Equation ◽  
High Frequency

scholarly journals Thin-layer solutions of the Helmholtz equation

2020 ◽  
pp. 1-15
Author(s):  
J. R. OCKENDON ◽  
R. H. TEW
Keyword(s):  
Wave Propagation ◽  
Thin Layer ◽  
Helmholtz Equation ◽  
Open Problem ◽  
High Frequency ◽  
Mathematical Structure ◽  
Mathematical Physics ◽  
Thin Layers ◽  
Frequency Wave ◽  
High Frequency Wave

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

scholarly journals High-frequency Bounds for the Helmholtz Equation Under Parabolic Trapping and Applications in Numerical Analysis

2020 ◽  
Vol 52 (1) ◽  
pp. 845-893 ◽  
Author(s):  
S. N. Chandler-Wilde ◽  
E. A. Spence ◽  
A. Gibbs ◽  
V. P. Smyshlyaev
Keyword(s):  
Numerical Analysis ◽  
Helmholtz Equation ◽  
High Frequency
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