TY - JOUR
T1 - The short-wave asymptotic behaviour of Green's function for the n-dimensional wave equation in an inhomogeneous medium
AU - Kucherenko, V. V.
PY - 1968
Y1 - 1968
N2 - IN the present paper the asymptotic behaviour of Green's function is studied for the wave equation [Δ + k2n2(x)]G = δ(x - x0), G = O( 1 |x| (N - 1> 2), ∂G ∂|x| + ik √EG = o( 1 |x| (N - 1) 2), (1) x = (x1, ..., xN), E = lim |x|→+∞ n2(x), n2 = E - V(x) > 0 in an N-dimensional space as k → + ∞. An asymptotic function will be constructed subject to the following conditions on the function n2(x).
AB - IN the present paper the asymptotic behaviour of Green's function is studied for the wave equation [Δ + k2n2(x)]G = δ(x - x0), G = O( 1 |x| (N - 1> 2), ∂G ∂|x| + ik √EG = o( 1 |x| (N - 1) 2), (1) x = (x1, ..., xN), E = lim |x|→+∞ n2(x), n2 = E - V(x) > 0 in an N-dimensional space as k → + ∞. An asymptotic function will be constructed subject to the following conditions on the function n2(x).
UR - http://www.scopus.com/inward/record.url?scp=49949129238&partnerID=8YFLogxK
U2 - 10.1016/0041-5553(68)90169-9
DO - 10.1016/0041-5553(68)90169-9
M3 - Artículo
SN - 0041-5553
VL - 8
SP - 294
EP - 302
JO - USSR Computational Mathematics and Mathematical Physics
JF - USSR Computational Mathematics and Mathematical Physics
IS - 4
ER -