 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V.Ph. Zhuravlev, "Ill-Posed Problems in Mechanics," Mech. Solids. 51 (5), 538-541 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
5 |
Pages |
538-541 |
| DOI |
10.3103/S0025654416050046 |
| Title |
Ill-Posed Problems in Mechanics |
| Author(s) |
V.Ph. Zhuravlev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, zhurav@ipmnet.ru) |
| Abstract |
The notion of ill-posed initial and boundary value problems for partial differential equations was introduced by Hadamard, who also presented the first example of an ill-posed problem for a specific partial differential equation. At the same time, there are numerous examples of ill-posed problems in any field of mechanics.
Hadamard and some of his successors believed that any ill-posed problem has no physical meaning and such problems should not be posed.
The present paper contains several examples of ill-posed problems. We show that if one deals with an applied problem, then overcoming the ill-posedness mathematically can help one to improve the structure in practice, which justifies the study of ill-posed problems. |
| Keywords |
ill-posed problem, dry friction, flutter |
| References |
| 1. | J. Hadamard,
The Cauchy Problem for Linear Partial Differential Equations of Hyperbolic Type
(Nauka, Moscow, 1978)
[in Russian]. |
| 2. | V. S. Vladimirov,
Equations of Mathematical Physics
(Nauka, Moscow, 1967)
[in Russian]. |
| 3. | F. A. Madvedev,
Early History of the Axiom of Choice
(Nauka, Moscow, 1982)
[in Russian]. |
| 4. | G. Coriolis,
Mathematical Theory of Phenomena of Billiard Games
(Carilian-Goeury, Paris, 1835; LKI, Moscow, 2007). |
| 5. | Yu. I. Neimark and N. A. Fufaev,
Dynamics of Nonholonomic Systems
(Nauka, Moscow, 1967; AMS, Providence, 1972). |
| 6. | V. Ph. Zhuravlev,
"Dynamics of a Heavy Homogeneous Ball on a Rough Plane,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 3-9 (2006)
[Mech. Solids (Engl. Transl.)
41 (6), 1-5 (2006)]. |
| 7. | A. A. Mailybaev and A. P. Seiranyan,
Multiparameter Problems of Stability. Theory and Applications in Mechanics
(Fizmatlit, Moscow, 2009)
[in Russian]. |
| 8. | Ya. G. Panovko and I. I. Gubanova,
Stability and Vibrations of Elastic Systems
(Nauka, Moscow, 1967)
[in Russian]. |
|
| Received |
14 May 2016 |
| Link to Fulltext |
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