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This article is cited in 7 scientific papers (total in 7 papers)
Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides
A. Yu. Anikina, S. Yu. Dobrokhotova, V. E. Nazaikinskiia, M. Rouleuxb a Ishlinsky Institute for Problems in Mechanics of the RAS, Moscow, Russia
b Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France
Abstract:
We develop a method for constructing semiclassical asymptotic solutions of inhomogeneous partial differential and pseudodifferential equations with localized right-hand sides. These problems are related to the asymptotics of Green's function for this type of operators, in particular, for the Helmholtz equation, which has been studied in numerous papers. The method is based on a constructive description of the corresponding Lagrangian manifolds and on the recently proposed new representations of the Maslov canonical operator in a neighborhood of Lagrangian singularities (caustics and caustic sets). The method underlies an analytic-numerical algorithm for constructing efficient asymptotic solutions to problems of the above-mentioned type in various fields of physics and continuum mechanics.
Keywords:
equation with right-hand side, Lagrangian manifold, semiclassical asymptotics, canonical operator.
Received: 13.09.2022 Revised: 13.09.2022
Citation:
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux, “Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides”, TMF, 214:1 (2023), 3–29; Theoret. and Math. Phys., 214:1 (2023), 1–23
Linking options:
https://www.mathnet.ru/eng/tmf10367https://doi.org/10.4213/tmf10367 https://www.mathnet.ru/eng/tmf/v214/i1/p3
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Abstract page: | 307 | Full-text PDF : | 42 | Russian version HTML: | 248 | References: | 38 | First page: | 20 |
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