The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides

Anikin, A.Y.; Dobrokhotov, S.Y.; Nazaikinskii, V.E.; Rouleux, M.

Авторы: Anikin A.Yu, Dobrokhotov S.Yu, Nazaikinskii V.E., Rouleux M.
Журнал: Doklady Mathematics
Том: 96
Номер: 1
Год издания: 2017
Издательство: Maik Nauka/Interperiodica Publishing
Местоположение издательства: Russian Federation
Первая страница: 406
Последняя страница: 410
Оригинальные версии: Канонический оператор Маслова на паре лагранжевых многообразий и асимптотика решений стационарных уравнений с локализованными правыми частями
DOI: 10.1134/S1064562417040275
Аннотация: The problem of constructing the asymptotics of the Green function for the Helmholtz operator h (2)Delta + n (2)(x), x a R (n) , with a small positive parameter h and smooth n (2)(x) has been studied by many authors; see, e.g., [1, 2, 4]. In the case of variable coefficients, the asymptotics was constructed by matching the asymptotics of the Green function for the equation with frozen coefficients and a WKB-type asymptotics or, in a more general situation, the Maslov canonical operator. The paper presents a different method for evaluating the Green function, which does not suppose the knowledge of the exact Green function for the operator with frozen variables. This approach applies to a larger class of operators, even when the right-hand side is a smooth localized function rather than a delta-function. In particular, the method works for the linearized water wave equations.
Добавил в систему: Левитин Александр Леонидович

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The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sidesстатья