Recent Progress in Operator Theory and Its Applications 2012
DOI: 10.1007/978-3-0348-0346-5_13
|View full text |Cite
|
Sign up to set email alerts
|

Scattering of a Plane Wave by “Hard-Soft” Wedges

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
5

Citation Types

1
21
0

Year Published

2014
2014
2018
2018

Publication Types

Select...
4

Relationship

0
4

Authors

Journals

citations
Cited by 4 publications
(22 citation statements)
references
References 5 publications
1
21
0
Order By: Relevance
“…In papers, we have proved for the first time the limiting amplitude principle (LAP) for the scattering by wedges with angle φ ∈ (0,2 π ) for a broad class of the profile functions: uφ(x,t)Aφ(x)eiωt,t, where u φ ( x , t ) is a unique solution from the classes introduced in previous studies . Namely, in other studies, the LAP was proved for DD, DN, and NN boundary conditions respectively for smooth incident waves and, in Komech et al, for distributional incident waves.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…In papers, we have proved for the first time the limiting amplitude principle (LAP) for the scattering by wedges with angle φ ∈ (0,2 π ) for a broad class of the profile functions: uφ(x,t)Aφ(x)eiωt,t, where u φ ( x , t ) is a unique solution from the classes introduced in previous studies . Namely, in other studies, the LAP was proved for DD, DN, and NN boundary conditions respectively for smooth incident waves and, in Komech et al, for distributional incident waves.…”
Section: Introductionmentioning
confidence: 99%
“…In the present paper, we analyze the Sommerfeld solution to the stationary diffraction by a half‐plane, which corresponds to the case φ = 0, (see also Sommerfeld. In this case, our results are not applicable directly. Nevertheless, we prove for the first time that even in this case, the LAP holds, ie, u0false(x,tfalse)Afalse(xfalse)eiωt,2emt, where A ( x ) is the Sommerfeld solution to the stationary diffraction problem with φ = 0.…”
Section: Introductionmentioning
confidence: 99%
“…On the other hand, the existence breaks down if we require an excessive regularity of the solution. This is why we have developed the rigorous theory , providing the uniqueness and existence of the solution in suitable functional spaces for the smooth Heaviside‐type function profile F ∈ C ∞ , supp F ⊂ [0, ∞ ), F ( s ) = 1 for s > s 0 > 0 of the incident wave. This approach relies on the method of complex characteristics .…”
Section: Introductionmentioning
confidence: 99%
“…Consequently, we can identify a significant number of publications where such analysis was taken for particular cases of wedge amplitudes and/or boundary conditions (cf., e.g., [2,7,8,9,10,11,12,13,18,21,22,33,34,35,42,48,44,45,46,49,50,55,56,58,60,66,72]). However, none of these listed papers contain final solvability results for the general problems in a rigourous mathematical Sobolev space setting as is done in the present paper.…”
Section: Introductionmentioning
confidence: 99%
“…Also, the limiting amplitude principle in the two-dimensional scattering of an incident plane harmonic wave by a wedge has recently been successfully applied, cf. [13,49,56].…”
Section: Introductionmentioning
confidence: 99%