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Found 29 Documents (Results 1–29)

Lagrangian manifolds and the construction of asymptotics for (pseudo)differential equations with localized right-hand sides. (English. Russian original) Zbl 1519.35061

Theor. Math. Phys. 214, No. 1, 1-23 (2023); translation from Teor. Mat. Fiz. 214, No. 1, 3-29 (2023).
MSC:  35C20 35S05 53D12
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Restricted partitions: the polynomial case. (English. Russian original) Zbl 1520.11085

Funct. Anal. Appl. 56, No. 4, 299-309 (2022); translation from Funkts. Anal. Prilozh. 56, No 4, 80-92 (2022).
MSC:  11N37 11B75 05C80
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Homogenization of the Cauchy problem for the wave equation with rapidly varying coefficients and initial conditions. (English) Zbl 1501.35031

Manuilov, Vladimir M. (ed.) et al., Differential equations on manifolds and mathematical physics. Dedicated to the memory of Boris Sternin. Selected papers based on the presentations of the conference on partial differential equations and applications, Moscow, Russia, November 6–9, 2018. Cham: Birkhäuser. Trends Math., 77-102 (2021).
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Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations. (English. Russian original) Zbl 1492.81056

Russ. Math. Surv. 76, No. 5, 745-819 (2021); translation from Usp. Mat. Nauk 76, No. 5, 3-80 (2021).
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Representation of Bessel functions by the Maslov canonical operator. (English. Russian original) Zbl 1471.81033

Theor. Math. Phys. 208, No. 2, 1018-1037 (2021); translation from Teor. Mat. Fiz. 208, No. 2, 196-217 (2021).
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Fock quantization of canonical transformations and semiclassical asymptotics for degenerate problems. (English) Zbl 1472.81099

Kielanowski, Piotr (ed.) et al., Geometric methods in physics XXXVIII. Workshop, Białowieża, Poland, June 30 – July 6, 2019. Cham: Birkhäuser. Trends Math., 187-195 (2020).
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Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp. (English. Russian original) Zbl 1483.53094

Math. Notes 108, No. 3, 318-338 (2020); translation from Mat. Zametki 108, No. 3, 334-359 (2020).
MSC:  53D12 41A60
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Efficient asymptotics in problems on the propagation of waves generated by localized sources in linear multidimensional inhomogeneous and dispersive media. (English. Russian original) Zbl 1450.35119

Comput. Math. Math. Phys. 60, No. 8, 1348-1360 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 8, 1394-1407 (2020).
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Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. (English. Russian original) Zbl 1441.81091

Theor. Math. Phys. 201, No. 3, 1742-1770 (2019); translation from Teor. Mat. Fiz. 201, No. 3, 382-414 (2019).
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Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem. (English. Russian original) Zbl 1420.35151

Math. Notes 104, No. 4, 471-488 (2018); translation from Mat. Zametki 104, No. 4, 483-504 (2018).
MSC:  35L20 35B40
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The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides. (English. Russian original) Zbl 1377.35062

Dokl. Math. 96, No. 1, 406-410 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 6, 624-628 (2016).
MSC:  35J05
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Punctured Lagrangian manifolds and asymptotic solutions of the linear water wave equations with localized initial conditions. (English. Russian original) Zbl 1516.35040

Math. Notes 101, No. 6, 1053-1060 (2017); translation from Mat. Zametki 101, No. 6, 936-942 (2017).
MSC:  35B25 35C20 35Q35
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On the asymptotics of the element counting function in an additive arithmetic semigroup with exponential counting function of prime generators. (English. Russian original) Zbl 1366.11105

Funct. Anal. Appl. 50, No. 4, 291-307 (2016); translation from Funkts. Anal. Prilozh. 50, No. 4, 55-75 (2016).
MSC:  11N45 11N80
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Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation. (English. Russian original) Zbl 1362.35170

Math. Notes 100, No. 5, 695-713 (2016); translation from Mat. Zametki 100, No. 5, 710-731 (2016).
MSC:  35L20 35L80 35B40
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The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary. (English. Russian original) Zbl 1330.53108

Math. Notes 96, No. 2, 248-260 (2014); translation from Mat. Zametki 96, No. 2, 261-276 (2014).
MSC:  53D12 35L05
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New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics. (English. Russian original) Zbl 1298.81091

Theor. Math. Phys. 177, No. 3, 1579-1605 (2013); translation from Teor. Mat. Fiz. 177, No. 3, 355-386 (2013).
MSC:  81Q20 81Q05
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Algebras with general commutation relations and their applications. I: Pseudodifferential equations with increasing coefficients. (English. Russian original) Zbl 0482.58028

J. Sov. Math. 15, 167-273 (1981); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 13, 5-144 (1979).
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