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- Title
Uniformization and Semiclassical Asymptotics for a Class of Equations Degenerating on the Boundary of a Manifold.
- Authors
Anikin, A. Yu.; Dobrokhotov, S. Yu.; Nazaikinskii, V. E.; Tolchennikov, A. A.
- Abstract
In the approximation of linearized shallow water equations, the free surface elevation for gravitational waves in a basin Ω of variable depth D(x) with gently sloping beaches is governed by a divergence form wave equation with the squared velocity c2 = gD(x) degenerating on ∂Ω = {x ∈ R2 : D = 0}. It is assumed that ∇D ≠ 0 for x ∈ ∂Ω. We consider a class of problems on manifolds with boundary generalizing this example. The phase space for such problems is the symplectic reduction of the cotangent bundle of a closed manifold of dimension higher by one. We construct semiclassical asymptotics for equations under consideration by using the quantization of reduction procedure applied to the Maslov canonical operator on Lagrangian submanifolds of the closed manifold.
- Subjects
SHALLOW-water equations; WAVE equation; PHASE space; GRAVITATIONAL waves; EQUATIONS; FREE surfaces; BEACHES
- Publication
Journal of Mathematical Sciences, 2023, Vol 270, Issue 4, p507
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-023-06363-8