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Found 82 Documents (Results 1–82)

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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\(C^*\)-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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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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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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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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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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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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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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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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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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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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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 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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Pseudodifferential operators on stratified manifolds. II. (English. Russian original) Zbl 1140.58008

Differ. Equ. 43, No. 5, 704-716 (2007); translation from Differ. Uravn. 43, No. 5, 685-696 (2007).
MSC:  58J40 47G30 35S35
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Homotopy classification of elliptic operators on stratified manifolds. (English. Russian original) Zbl 1327.58025

Dokl. Math. 73, No. 3, 407-411 (2006); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 408, No. 5, 591-595 (2006).
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Pseudodifferential operators on manifolds with singularities and localization. (English. Russian original) Zbl 1272.58012

Dokl. Math. 71, No. 3, 457-460 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 402, No. 6, 743-747 (2005).
MSC:  58J40 35S05 47G30
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On the index of differential operators on manifolds with edges. (English. Russian original) Zbl 1125.58303

Dokl. Math. 69, No. 1, 68-71 (2004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 394, No. 3, 309-312 (2004).
MSC:  58J22 35J30
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On the definition of pseudodifferential operators on manifolds with singularities. (English. Russian original) Zbl 1125.58305

Dokl. Math. 69, No. 1, 41-44 (2004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 394, No. 2, 162-165 (2004).
MSC:  58J40 35S05
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A remark on surgery in index theory of elliptic operators. (English) Zbl 1039.35153

de Gosson, Maurice (ed.), Jean Leray ’99 conference proceedings. The Karlskrona conference, Sweden, August 1999 in honor of Jean Leray. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1378-7/hbk). Math. Phys. Stud. 24, 363-372 (2003).
MSC:  35S30 35S05 47G30
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Algebras of pseudodifferential operators on manifolds with singularities. (English. Russian original) Zbl 1065.47045

Dokl. Math. 63, No. 3, 302-305 (2001); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 378, No. 1, 14-17 (2001).
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The index of Fourier integral operators on manifolds with conical singularities. (English. Russian original) Zbl 1004.58015

Izv. Math. 65, No. 2, 329-355 (2001); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 2, 127-154 (2001).
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Localization and surgery in the index theory of elliptic operators. (English. Russian original) Zbl 1054.58014

Dokl. Math. 61, No. 1, 13-16 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 370, No. 1, 19-23 (2000).
MSC:  58J20 35J40
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The index of quantized contact transformations on manifolds with conical singularities. (English. Russian original) Zbl 1072.58502

Dokl. Math. 60, No. 2, 243-245 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 368, No. 5, 598-600 (1999).
MSC:  58J20 35S30 58J40
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Spectral boundary value problems and elliptic equations on manifolds with singularities. (English. Russian original) Zbl 0962.58008

Dokl. Math. 60, No. 1, 97-99 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 367, No. 5, 597-599 (1999).
MSC:  58J32 35J55
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Spectral boundary value problems and elliptic equations on singular manifolds. (English. Russian original) Zbl 1040.58500

Differ. Equations 34, No. 5, 696-710 (1998); translation from Differ. Uravn. 34, No. 5, 695-708 (1998).
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Analytic singularities of solutions of differential equations. (English) Zbl 0792.58039

Kashiwara, Masaki (ed.) et al., D-modules and microlocal geometry. Proceedings of the international conference, held at the University of Lisbon, Portugal, Oct. 29-Nov. 2, 1990. Berlin: Walter de Gruyter. 187-198 (1993).
MSC:  58J47 32S40 35A07
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Introduction to Maslov’s operational method (applications). (English) Zbl 0827.35006

Borisovich, Yu. G. (ed.), Problems of geometry, topology and mathematical physics. Voronezh: Izdatel’stvo Voronezhskogo Universiteta. Nov. Global’nom Anal. 51-64 (1992).
MSC:  35A25 76X05
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Local solvability of differential equations in spaces of many-valued analytic functions. (English. Russian original) Zbl 0769.35002

Differ. Equations 27, No. 1, 82-91 (1991); translation from Differ. Uravn. 27, No. 1, 103-114 (1991).
Reviewer: M.Biroli (Monza)
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Asymptotics of operator and pseudo-differential equations. Transl. from the Russian. (English) Zbl 0702.35002

Contemporary Soviet Mathematics. New York etc.: Consultants Bureau. vi, 313 p. $ 79.50 (1988).
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Fourier integral operators and the canonical operator. (English. Russian original) Zbl 0507.58043

Russ. Math. Surv. 36, No. 2, 93-161 (1981); translation from Usp. Mat. Nauk 36, No. 2(218), 81-140 (1981).
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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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