Operator Theory, Pseudo-Differential Equations, and Mathematical Physics 2012
DOI: 10.1007/978-3-0348-0537-7_6
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Functions of Noncommuting Operators in an Asymptotic Problem for a 2D Wave Equation with Variable Velocity and Localized Right-hand Side

Abstract: In the present paper, we use the theory of functions of noncommuting operators, also known as noncommutative analysis (which can be viewed as a far-reaching generalization of pseudodifferential operator calculus), to solve an asymptotic problem for a partial differential equation and show how, starting from general constructions and operator formulas that seem to be rather abstract from the viewpoint of differential equations, one can end up with very specific, easy-to-evaluate expressions for the solution, us… Show more

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Cited by 7 publications
(1 citation statement)
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“…An important step towards greater sophistication of the proposed 1D model would be to refine the boundary regime more appropriately to represent the tsunami wave. For instance, in [20,28], function (29), multiplied by a trigonometric function, was proposed. Such a modification allows computing the Fourier image and adjusting the working formula (34).…”
Section: Discussionmentioning
confidence: 99%
“…An important step towards greater sophistication of the proposed 1D model would be to refine the boundary regime more appropriately to represent the tsunami wave. For instance, in [20,28], function (29), multiplied by a trigonometric function, was proposed. Such a modification allows computing the Fourier image and adjusting the working formula (34).…”
Section: Discussionmentioning
confidence: 99%