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

Sommerfeld's solution as the limiting amplitude and asymptotics for narrow wedges

“…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: 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.…”

“…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, where A ( x ) is the Sommerfeld solution to the stationary diffraction problem with φ = 0.…”

On the Keller‐Blank solution to the scattering problem of pulses by wedges

“…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 .…”

Wave diffraction by wedges having arbitrary aperture angle

“…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.…”

“…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].…”