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IssuesArchive of Issues2016-5pp.538-541

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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
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