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Found 160 Documents (Results 1–100)

Nonlinear effects and run-up of coastal waves generated by billiards with semi-rigid walls in the framework of shallow water theory. (English. Russian original) Zbl 07781666

Proc. Steklov Inst. Math. 322, 105-117 (2023); translation from Tr. Mat. Inst. Steklova 322, 111-123 (2023).
MSC:  76B15 76M45 86A05
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Uniformization and semiclassical asymptotics for a class of equations degenerating on the boundary of a manifold. (English. Russian original) Zbl 1512.35066

J. Math. Sci., New York 270, No. 4, 507-530 (2023); translation from Probl. Mat. Anal. 122, 5-24 (2023).
MSC:  35B40 53D12 76B15
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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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\(C^*\)-algebras of transmission problems and elliptic boundary value problems with shift operators. (English. Russian original) Zbl 1493.58009

Math. Notes 111, No. 5, 701-721 (2022); translation from Mat. Zametki 111, No. 5, 692-716 (2022).
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Nonstandard Liouville tori and caustics in asymptotics in the form of Airy and Bessel functions for 2D standing coastal waves. (English. Russian original) Zbl 1485.35307

St. Petersbg. Math. J. 33, No. 2, 185-205 (2022); translation from Algebra Anal. 33, No. 2, 5-34 (2021).
MSC:  35P20 35B40 35J25
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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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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. (English) Zbl 1478.35002

Trends in Mathematics. Cham: Birkhäuser (ISBN 978-3-030-37325-2/hbk; 978-3-030-37326-9/ebook). x, 338 p. (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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Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics. (English. Russian original) Zbl 1455.76019

Math. Notes 107, No. 5, 847-853 (2020); translation from Mat. Zametki 107, No. 5, 780-786 (2020).
MSC:  76B15 76M45 35Q35
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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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Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\). (English. Russian original) Zbl 1452.34085

Proc. Steklov Inst. Math. 306, 74-89 (2019); translation from Tr. Mat. Inst. Steklova 306, 83-99 (2019).
MSC:  34L10 34L15
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Maslov’s canonical operator in problems on localized asymptotic solutions of hyperbolic equations and systems. (English. Russian original) Zbl 1432.35025

Math. Notes 106, No. 3, 402-411 (2019); translation from Mat. Zametki 106, No. 3, 424-435 (2019).
MSC:  35B40 58J40 53D12
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Asymptotics, related to billiards with semi-rigid walls, of eigenfunctions of the \(\nabla D(x)\nabla\) operator in dimension 2 and trapped coastal waves. (English. Russian original) Zbl 1426.37049

Math. Notes 105, No. 5, 789-794 (2019); translation from Mat. Zametki 105, No. 5, 792-797 (2019).
MSC:  37J35 37J10 34L10 34L20
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Asymptotic eigenfunctions of the operator \(\nabla D(x)\nabla\) defined in a two-dimensional domain and degenerating on its boundary and billiards with semi-rigid walls. (English. Russian original) Zbl 1418.37094

Differ. Equ. 55, No. 5, 644-657 (2019); translation from Differ. Uravn. 55, No. 5, 660-672 (2019).
MSC:  37J35 37J05 37D50 53D12 53D25 35P05
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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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Homogenization method in the problem of long wave propagation from a localized source in a basin over an uneven bottom. (English. Russian original) Zbl 1418.76043

Differ. Equ. 54, No. 8, 1057-1072 (2018); translation from Differ. Uravn. 54, No. 8, 1075-1089 (2018).
MSC:  76M50 76B15 76M45
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Analogue of Maslov’s canonical operator for localized functions and its applications to the description of rapidly decaying asymptotic solutions of hyperbolic equations and systems. (English. Russian original) Zbl 1407.35028

Dokl. Math. 97, No. 2, 177-180 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 479, No. 6, 611-615 (2018).
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Method for the analysis of long water waves taking into account reflection from a gently sloping beach. (English. Russian original) Zbl 1440.76014

J. Appl. Math. Mech. 81, No. 1, 21-28 (2017); translation from Prikl. Mat. Mekh. 81, No. 1, 33-44 (2017).
MSC:  76B15 76-04
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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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On the limit shape of elements of an arithmetic semigroup with an exponentially growing counting function of basis elements. (English. Russian original) Zbl 1430.11136

Dokl. Math. 95, No. 3, 226-229 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 474, No. 3, 277-280 (2017).
MSC:  11N45 60F10
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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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Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach. (English. Russian original) Zbl 1372.35180

Math. Notes 101, No. 5, 802-814 (2017); translation from Mat. Zametki 101, No. 5, 700-715 (2017).
MSC:  35L20 76E20 86A05
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New integral representations of the Maslov canonical operator in singular charts. (English. Russian original) Zbl 1369.81033

Izv. Math. 81, No. 2, 286-328 (2017); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 81, No. 2, 53-96 (2017).
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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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On the Bose-Maslov statistics in the case of infinitely many degrees of freedom. (English. Russian original) Zbl 1357.11095

Dokl. Math. 93, No. 3, 326-328 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 468, No. 6, 618-621 (2016).
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Maslov’s canonical operator in arbitrary coordinates on the Lagrangian manifold. (English. Russian original) Zbl 1345.53083

Dokl. Math. 93, No. 1, 99-102 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 466, No. 6, 641-644 (2016).
MSC:  53D12 81Q20
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Simple exact and asymptotic solutions of the 1D run-up problem over a slowly varying (quasiplanar) bottom. (English) Zbl 1329.35246

Agliari, Elena (ed.) et al., Theory and applications in mathematical physics. Conference in honor of B. Tirozzi’s 70th birthday. Hackensack, NJ: World Scientific (ISBN 978-981-4713-27-6/hbk; 978-981-4713-29-0/ebook). 29-47 (2016).
MSC:  35Q35 76B15 76M45
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Handbook of linear partial differential equations for engineers and scientists. 2nd edition. (English) Zbl 1329.35001

Boca Raton, FL: CRC Press (ISBN 978-1-4665-8145-6/hbk; 978-1-4665-8149-4/ebook). xxxiv, 1609 p. (2016).
MSC:  35-00 00A06 35-01
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On a homogenization method for differential operators with oscillating coefficients. (English. Russian original) Zbl 1326.35022

Dokl. Math. 91, No. 2, 227-231 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 461, No. 5, 516-520 (2015).
MSC:  35B27 35L15
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Fourier integrals and a new representation of Maslov’s canonical operator near caustics. (English) Zbl 1320.81058

Khruslov, E. (ed.) et al., Spectral theory and differential equations: V. A. Marchenko’s 90th anniversary collection. Providence, RI: American Mathematical Society (AMS); (ISBN 978-1-4704-1683-6/hbk). Translations. Series 2. American Mathematical Society 233; Advances in the Mathematical Sciences 66, 95-115 (2014).
MSC:  81Q20 35S30 53D12
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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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Maslov’s canonical operator, Hörmander’s formula, and localization of the Berry-Balazs solution in the theory of wave beams. (English. Russian original) Zbl 1323.81031

Theor. Math. Phys. 180, No. 2, 894-916 (2014); translation from Teor. Mat. Fiz. 180, No. 2, 162-188 (2014).
MSC:  81Q05 35C05 35Q41
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The localization problem in index theory of elliptic operators. (English) Zbl 1297.58001

Pseudo-Differential Operators. Theory and Applications 10. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0509-4/pbk; 978-3-0348-0510-0/ebook). viii, 117 p. (2014).
MSC:  58-02 46L80 58J22
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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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Functions of noncommuting operators in an asymptotic problem for a 2D wave equation with variable velocity and localized right-hand side. (English) Zbl 1263.35154

Karlovich, Yuri I. (ed.) et al., Operator theory, pseudo-differential equations, and mathematical physics. The Vladimir Rabinovich anniversary volume. Dedicated to his 70th birthday. Basel: Birkhäuser (ISBN 978-3-0348-0536-0/hbk; 978-3-0348-0537-7/ebook). Operator Theory: Advances and Applications 228, 95-125 (2013).
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The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac-type operators with classical boundary conditions. (English. Russian original) Zbl 1282.82064

Theor. Math. Phys. 172, No. 3, 1263-1277 (2012); translation from Teor. Mat. Fiz. 172, No. 3, 437-453 (2012).
MSC:  82D80 81Q05 37B30
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Asymptotic solutions of the two-dimensional model wave equation with degenerating velocity and localized initial data. (English. Russian original) Zbl 1230.35057

St. Petersbg. Math. J. 22, No. 6, 895-911 (2011); translation from Algebra Anal. 22, No. 6, 67-90 (2010).
MSC:  35L15 35C20 78A05
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On the Poincaré isomorphism in \(K\)-theory on manifolds with edges. (English. Russian original) Zbl 1305.19003

J. Math. Sci., New York 170, No. 2, 238-250 (2010); translation from Sovrem. Mat., Fundam. Napravl. 34, 109-120 (2009).
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Noncommutative geometry and classification of elliptic operators. (English. Russian original) Zbl 1301.58015

J. Math. Sci., New York 164, No. 4, 603-636 (2010); translation from Sovrem. Mat., Fundam. Napravl. 29, 131-164 (2008).
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On the distribution of integer random variables related by a certain linear inequality. III. (English. Russian original) Zbl 1202.82006

Math. Notes 83, No. 6, 804-820 (2008); translation from Mat. Zametki 83, No. 6, 880-898 (2008).
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On the index of nonlocal elliptic operators. (English. Russian original) Zbl 1160.58010

Dokl. Math. 77, No. 3, 441-445 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 420, No. 5, 592-597 (2008).
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Elliptic theory on manifolds with corners. II: homotopy classification and \(K\)-homology. (English) Zbl 1205.58018

Burghelea, Dan (ed.) et al., \(C^*\)-algebras and elliptic theory II. Selected papers of the international conference, Bȩdlewo, Poland, January 2006. Basel: Birkhäuser (ISBN 978-3-7643-8603-0/hbk). Trends in Mathematics, 207-226 (2008).
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Elliptic theory on manifolds with corners. I: Dual manifolds and pseudodifferential operators. (English) Zbl 1205.58017

Burghelea, Dan (ed.) et al., \(C^*\)-algebras and elliptic theory II. Selected papers of the international conference, Bȩdlewo, Poland, January 2006. Basel: Birkhäuser (ISBN 978-3-7643-8603-0/hbk). Trends in Mathematics, 183-206 (2008).
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Elliptic theory and noncommutative geometry. Nonlocal elliptic operators. (English) Zbl 1158.58013

Operator Theory: Advances and Applications 183. Advances in Partial Differential Equations. Basel: Birkhäuser (ISBN 978-3-7643-8774-7/hbk). xii, 224 p. (2008).
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On the homotopy classification of elliptic operators on manifolds with corners. (English. Russian original) Zbl 1156.58011

Dokl. Math. 75, No. 2, 186-189 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 413, No. 1, 16-19 (2007).
MSC:  58J40 58J05
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