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22 results on '"Arlen Mikhailovich Il'in"'

1. The asymptotics of a solution of a parabolic equation as time increases without bound

Author

Arlen Mikhailovich Il'in and Denis Olegovich Degtyarev

Subjects
SMALL PARAMETER, Algebra and Number Theory, Mathematical analysis, Bibliography, Order (group theory), BOUNDARY-VALUE PROBLEM, METHOD OF MATCHING, Boundary value problem, ASYMPTOTIC EXPANSION, Power (physics), Mathematics
Abstract

A boundary-value problem for a second order parabolic equation on a half-line is considered. A uniform asymptotic approximation to a solution to within any power of t-1 is constructed and substantiated. © 2012 RAS(DoM) and LMS.

Published
2012

4. The asymptotic behaviour of the solution to a system of differential equations with a small parameter and singular initial point

Author

Arlen Mikhailovich Il'in, Oleg Yu Khachay, and Yurii Alekseevich Leonychev

Subjects
Examples of differential equations, Singular perturbation, Algebra and Number Theory, Singular solution, Mathematical analysis, Asymptotology, Initial value problem, Exponential integrator, Asymptotic expansion, Method of matched asymptotic expansions, Mathematics
Abstract

The initial value problem for a system of nonlinear ordinary differential equations with a small parameter multiplying the highest derivative is investigated. In a neighbourhood of the initial point the asymptotic behaviour of the solution has quite a complicated structure. A uniform asymptotic approximation to the solution up to an arbitrary power of the small parameter is constructed and substantiated. Bibliography: 3 titles.

Published
2010

5. Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe. II. Large values of the parametert

Author

Arlen Mikhailovich Il'in and Bulat I Suleĭmanov

Subjects
Cusp (singularity), Asymptotic analysis, Algebra and Number Theory, Abel's identity, Mathematical analysis, Bibliography, Asymptotology, Asymptotic formula, Abel's test, Differential (mathematics), Mathematics
Abstract

An asymptotic formula as for the solution of the ordinary differential Abel's equation of the first kind , which is uniform in the x-variable, is constructed and substantiated. Bibliography: 13 titles.

Published
2007

7. Stanislav Ivanovich Pokhozhaev (on his 70th birthday)

Author

Oleg Vladimirovich Besov, L D Kudryavtsev, Arlen Mikhailovich Il'in, L. Veron, Enzo Mitidieri, Sergei M Nikol'skii, A. Tesei, Lev Vasil'evich Ovsyannikov, and Vladimir Aleksandrovich Il'in

Subjects
General Mathematics, Art history, Ivanovich, Mathematics
Published
2006

8. Asymptotic behaviour of a special solution of Abel's equation relating to a cusp catastrophe

Author

B. I. Suleimanov and Arlen Mikhailovich Il'in

Subjects
Stochastic partial differential equation, Algebra and Number Theory, Liénard equation, Differential equation, Weak solution, Abel's identity, Mathematical analysis, First-order partial differential equation, Exact differential equation, Mathematics, Separable partial differential equation
Abstract

A special solution of Abel's ordinary differential equation of the first kind is considered, which describes the behaviour of a broad spectrum of solutions of partial differential equations with a small parameter in the neighbourhood of cusp points of their slowly varying equilibrium positions. The existence of this special solution is demonstrated; an asymptotic formula for it as , is constructed and substantiated.

Published
2006

11. Birth of step-like contrast structures connected with a cusp catastrophe

Author

B. I. Suleimanov and Arlen Mikhailovich Il'in

Subjects
Stochastic partial differential equation, Cusp (singularity), Algebra and Number Theory, Linear differential equation, Differential equation, Ordinary differential equation, Weak solution, Mathematical analysis, First-order partial differential equation, Universal differential equation, Mathematics
Abstract

A special solution of the ordinary differential equation u''{sub xx}=u{sup 3}-tu-x is considered which relates to solutions of a broad spectrum of partial differential equations with a small parameter. The function u(x,t) is the dominant term of asymptotic expressions with respect to the small parameter for these solutions near cusp points of the limiting solution. The existence of this special function u(x,t) is proved; its uniform asymptotics at infinity are constructed and substantiated.

Published
2004

13. Олейник Ольга Арсеньевна (некролог)

Author

Victor Antonovich Sadovnichii, Yurii S Osipov, L D Kudryavtsev, Tat'yana Ardolionovna Shaposhnikova, Nikolai Khristovich Rozov, V. A. Kondrat’ev, Evgenii Frolovich Mishchenko, Andrei Andreevich Shkalikov, Tat'yana Dmitrievna Venttsel', Gregory A. Chechkin, Lyudvig Dmitrievich Faddeev, Vasilii S Vladimirov, Aleksey Stanislavovich Shamaev, Sergei M Nikol'skii, Arlen Mikhailovich Il'in, Evgenii Vladimirovich Radkevich, Vladimir Aleksandrovich Il'in, and Vasilii Vasil'evich Zhikov

Subjects
Obituary, Medicinal chemistry, Mathematics
Published
2003

17. Анатолий Сергеевич Калашников (некролог)

Author

V. A. Kondrat’ev, Arkadii Anatol'evich Mal'tsev, Tat'yana Ardolionovna Shaposhnikova, Olga Arsen'evna Oleinik, Nikolai Khristovich Rozov, Arlen Mikhailovich Il'in, Stanislav Ivanovich Pokhozhaev, Valentin Petrovich Mikhailov, Yulii Andreevich Dubinskii, Tat'yana Dmitrievna Venttsel', and Gregory A. Chechkin

Subjects
Materials science, Theology, Obituary
Published
2000

21. Рамиль Фаритович Бикбаев (некоролог)

Author

Leonid Anatol'evich Kalyakin, Victor Yur'evich Novokshenov, Sergei Yur'evich Dobrokhotov, Alexander Its, Aleksander Ivanovich Bobenko, Alexey Borisovich Shabat, Arlen Mikhailovich Il'in, and Vladimir Borisovich Matveev

Subjects
Physics, Obituary, Theology
Published
1996

22. On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit

Author

Arlen Mikhailovich Il'in and R R Gadyl'shin

Subjects
Singular perturbation, Asymptotic analysis, 34E15, 34E05, 35J25, General Mathematics, Mathematical analysis, FOS: Physical sciences, Mathematical Physics (math-ph), Method of matched asymptotic expansions, Neumann boundary condition, Asymptotology, Perturbation theory, Asymptotic expansion, Mathematical Physics, Mathematics
Abstract

The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small para- meter 0

Published
2002
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