Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side

2012/04/12 by S. Dobrokhotov, Dobrokhotov, S., D. Minenkov +5
Mathematics · Physics and Astronomy · #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Primary 35L05 #Secondary 81Q20 #math-ph #math.AP #math.FA #math.MP #msc:35L05 #msc:35Q35 #msc:81Q20

paper · pdf · doi:10.48550/arxiv.1204.2639

29 pages, 4 figures. Accepted for publication in The Vladimir Rabinovich Anniversary Volume of "Operator Theory: Advances and Applications" (Birkhäuser)

arxiv created 2012/04/12 · arxiv updated 2012/04/13

Abstract

We use the theory of functions of noncommuting operators (noncommutative analysis) 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, useful, e.g., in the tsunami wave problem.

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