This article is cited in 2 scientific papers (total in 2 papers)
On the principle of limiting amplitude
B. R. Vainberg
In this paper we give a formulation and proof of a principle of limiting amplitude which allows one to select all of those solutions of the corresponding elliptic equation (of arbitrary order) which are obtained by means of the radiation conition and the principle of limiting absorption. In particular, the case when the latter two principles select more than two solutions is considered. The formulation of this new principle is connected with the transition to a certain nonstationary equation with several new variables, for which a Goursat-type problem is studied. The presence of several additional variables gives rise to a new resonance-like effect, which is also investigated.
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Mathematics of the USSR-Sbornik, 1971, 15:1, 89–108
MSC: Primary 35J30; Secondary 35J05
B. R. Vainberg, “On the principle of limiting amplitude”, Mat. Sb. (N.S.), 86(128):1(9) (1971), 90–109; Math. USSR-Sb., 15:1 (1971), 89–108
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\paper On the principle of limiting amplitude
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
B. R. Vainberg, “On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems”, Math. USSR-Sb., 21:2 (1973), 221–239
B. R. Vainberg, “On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems”, Russian Math. Surveys, 30:2 (1975), 1–58
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