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

This article is cited in 8 scientific papers (total in 8 papers)

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

Sergey I. Senashova, Alexander Yakhnob

a Siberian State Aerospace University, Krasnoyarsk, Russia
b Departamento de Matemáticas, CUCEI, Universidad de Guadalajara, 44430, Mexico

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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Full text: http://emis.mi.ras.ru/.../071
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Bibliographic databases:

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
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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  crossref  mathscinet  zmath  isi  elib  scopus
    2. Senashov S.I., Yakhno A., “Conservation Laws of Three-Dimensional Perfect Plasticity Equations Under Von Mises Yield Criterion”, Abstract Appl. Anal., 2013, 702132  crossref  mathscinet  isi  elib  scopus
    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  crossref  adsnasa  isi  elib  scopus
    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  mathnet  crossref
    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  mathnet  crossref  crossref  isi  elib
    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  crossref  isi  elib  scopus
    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  crossref  mathscinet  isi  scopus
    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  mathnet  crossref
  • Symmetry, Integrability and Geometry: Methods and Applications
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