The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary

2014 ◽  
Vol 96 (1-2) ◽  
pp. 248-260 ◽  
Author(s):  
V. E. Nazaikinskii
Keyword(s):  
Wave Equation ◽  
Phase Space ◽  
Maslov Canonical Operator ◽  
Canonical Operator ◽  
Lagrangian Manifolds

New integral representations of the Maslov canonical operator in singular charts

2017 ◽  
Vol 81 (2) ◽  
pp. 286-328 ◽  
Author(s):  
S Yu Dobrokhotov ◽  
V E Nazaikinskii ◽  
A I Shafarevich
Keyword(s):  
Integral Representations ◽  
Maslov Canonical Operator ◽  
Canonical Operator

scholarly journals A Phase Space Transform Adapted to the Wave Equation

2007 ◽  
Vol 32 (7) ◽  
pp. 1065-1101 ◽  
Author(s):  
Dan-Andrei Geba ◽  
Daniel Tataru
Keyword(s):  
Wave Equation ◽  
Phase Space

Representations of rapidly decaying functions by the Maslov canonical operator

2007 ◽  
Vol 82 (5-6) ◽  
pp. 713-717 ◽  
Author(s):  
S. Yu. Dobrokhotov ◽  
B. Tirozzi ◽  
A. I. Shafarevich
Keyword(s):  
Maslov Canonical Operator ◽  
Canonical Operator

Canonical Operator on Punctured Lagrangian Manifolds

2021 ◽  
Vol 28 (1) ◽  
pp. 22-36
Author(s):  
S. Yu. Dobrokhotov ◽  
V. E. Nazaikinskii ◽  
A. I. Schafarevich
Keyword(s):  
Canonical Operator ◽  
Lagrangian Manifolds

RELATIVISTIC PARTICLE WITH CURVATURE IN AN EXTERNAL ELECTROMAGNETIC FIELD

1991 ◽  
Vol 06 (22) ◽  
pp. 3989-3996 ◽  
Author(s):  
V.V. NESTERENKO
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Phase Space ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Canonical Quantization ◽  
Hamiltonian Formalism ◽  
External Electromagnetic Field ◽  
Operator Form ◽  
Complete Set

A model of a relativistic particle with curvature interacting with an external electromagnetic field in a “minimal way” is investigated. The generalized Hamiltonian formalism for this model is constructed. A complete set of the constraints in the phase space is obtained and then divided into first- and second-class constraints. On this basis the canonical quantization of the model is considered. A wave equation in the operator form, resembling the Dirac equation in an external electromagnetic field, is obtained. The massless version of this model is briefly discussed.

Compact attractor for a nonlinear wave equation with critical exponent

1990 ◽  
Vol 115 (1-2) ◽  
pp. 61-64 ◽  
Author(s):  
Orlando Lopes
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Phase Space ◽  
Critical Exponent ◽  
Growth Condition ◽  
Nonlinear Wave Equation ◽  
Compact Attractor ◽  
Homogeneous Wave ◽  
Coercive Condition ◽  
Homogeneous Wave Equation

SynopsisIn this paper we study the existence of a compact attractor for the solutions of the equation utt − Δu + cut + f(u) = h(t, x), x ∊ ℝ3. The phase space is H1 × L2 and periodicity in the x-variables is taken as a boundary condition. Besides the usual coercive condition, we assume f satisfies the growth condition |f′(u)|≦ a + bu2; this growth condition is critical because the embedding H1 → L6 is not compact. In the proof we use an Lp − H1.q estimate for the linear homogeneous wave equation.

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