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 SIGMA, 2012, Volume 8, 071, 16 pages (Mi sigma748)

Conservation laws, hodograph transformation and boundary value problems of plane plasticity

Sergey I. Senashova, Alexander Yakhnob

a Siberian State Aerospace University, Krasnoyarsk, Russia

Abstract: For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permits to construct the characteristic lines in domains, where Jacobian of hodograph transformations is equal to zero. Moreover, the conservation laws give all solutions of the linearized system. Some examples from the gas dynamics and theory of plasticity are considered.

Keywords: conservation laws; hodograph transformation; Riemann method; plane plasticity; boundary value problem.

DOI: https://doi.org/10.3842/SIGMA.2012.071

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ArXiv: 1210.????
MSC: 35L65; 58J45; 74G10
Received: April 18, 2012; in final form September 29, 2012; Published online October 13, 2012
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Citation: Sergey I. Senashov, Alexander Yakhno, “Conservation laws, hodograph transformation and boundary value problems of plane plasticity”, SIGMA, 8 (2012), 071, 16 pp.

Citation in format AMSBIB
\Bibitem{SenYak12} \by Sergey I. Senashov, Alexander Yakhno \paper Conservation laws, hodograph transformation and boundary value problems of plane plasticity \jour SIGMA \yr 2012 \vol 8 \papernumber 071 \totalpages 16 \mathnet{http://mi.mathnet.ru/sigma748} \crossref{https://doi.org/10.3842/SIGMA.2012.071} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3007288} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312372300001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867818756} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Senashov S.I., Yakhno A., “Some Symmetry Group Aspects of a Perfect Plane Plasticity System”, J. Phys. A-Math. Theor., 46:35 (2013), 355202
2. Senashov S.I., Yakhno A., “Conservation Laws of Three-Dimensional Perfect Plasticity Equations Under Von Mises Yield Criterion”, Abstract Appl. Anal., 2013, 702132
3. Morad A.M., Zhukov M.Yu., “the Motion of a Thin Liquid Layer on the Outer Surface of a Rotating Cylinder”, Eur. Phys. J. Plus, 130:1 (2015), 8
4. Sergey I. Senashov, Alexander V. Kondrin, Olga N. Cherepanova, “On elastoplastic torsion of a rod with multiply connected cross-section”, Zhurn. SFU. Ser. Matem. i fiz., 8:3 (2015), 343–351
5. M. S. Elaeva, M. Yu. Zhukov, E. V. Shiryaeva, “Interaction of weak discontinuities and the hodograph method as applied to electric field fractionation of a two-component mixture”, Comput. Math. Math. Phys., 56:8 (2016), 1440–1453
6. Senashov S.I., Yakhno A., “Application of conservation laws to Dirichlet problem for elliptic quasilinear systems”, Int. J. Non-Linear Mech., 85 (2016), 1–5
7. Albright E.J. Ramsey S.D. Schmidt J.H. Baty R.S., “Scaling Symmetries in Elastic-Plastic Dynamic Cavity-Expansion Equations Using the Isovector Method”, Q. J. Mech. Appl. Math., 71:1 (2018), 25–45
8. Sergei I. Senashov, Irina L. Savostyanova, Olga N. Cherepanova, “Solution of boundary value problems of plasticity with the use of conservation laws”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 356–363
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