Skip to main content
  • 456 Accesses

Abstract

The existence of conservation laws for a system of partial differential equations is of great help in investigating the properties of the solutions. For example, such is the case in proving existence of solutions, study of singularities, analysis of integrability properties of the system. Of course the more conservation laws are known for a system, the more tools are available for such investigations. This is a natural motivation for the growing attention addressed to the subject (cf. [1, 2, 3, 4]).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Olver, P. J.: Applications of Lie Groups to Differential Equations. New York: Springer, 1986.

    Book  MATH  Google Scholar 

  2. Ovsiannikov, L. V.: Group Analysis of Differential Equations. New York: Academic Press 1982.

    MATH  Google Scholar 

  3. Anderson, R. L., Ibragimov, N. H.: Lie-Bäcklund Transformations in Applications. Philadelphia: SIAM 1979.

    Book  MATH  Google Scholar 

  4. Fushchich, V. I., Nikitin, A. G.: New and old symmetries of the Maxwell and Dirac equations. Sov. J. Part. Nucl. 14, 1–22 (1983).

    MathSciNet  Google Scholar 

  5. Jiang, Q.: Conservation laws in viscoelastostatics. Acta Mechanica 56, 219–227 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  6. Jiang, Q.: Conservation laws in linear viscoelastodynamics. J. Elasticity 16, 213–219 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  7. Caviglia, G., Morro, A.: A general approach to conservation laws in viscoelasticity. Acta Mechanica 66, 191–204 (1988).

    MathSciNet  Google Scholar 

  8. Zhang, Ch.: On some conservation laws in transient elastodynamics. Acta Mechanica 83, 187–193 (1990).

    Article  MathSciNet  Google Scholar 

  9. Caviglia, G., Morro, A.: Conservation laws in viscoelasticity. Quart. Appl. Math. 48, 503–516 (1990).

    MathSciNet  MATH  Google Scholar 

  10. Caviglia, G., Morro, A.: On the generation of conservation laws in viscoelasticity. Acta Mechanica 81, 91–95 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  11. Caviglia, G., Morro, A.: Conservation laws in heat conduction with memory. Rend. Matem. 9, 369–381 (1989).

    MathSciNet  MATH  Google Scholar 

  12. Signorini, A.: Alcune proprietà di media nella elastostatica ordinaria. Rend. Accad. Naz. Lincei 15, 151–156 (1932).

    Google Scholar 

  13. Truesdell, C., Toupin, R.: The classical field theories. In: Encyclopedia of Physics (Flügge, S., ed.), III/l. Berlin: Springer 1960.

    Google Scholar 

  14. Caviglia, G.: Symmetry transformations, isovectors, and conservation laws. J. Math. Phys. 27, 972–978 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  15. Caviglia, G.: Composite variational principles and the determination of conservation laws. J. Math. Phys. 29, 812–816 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  16. Olver, P. J.: Conservation laws in elasticity. I. General results. Arch. Rational Mech. Anal. 85, 112–129 (1984).

    Google Scholar 

  17. Gurtin, M. E., Sternberg, E.: On the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 11, 291–356 (1963).

    Article  MathSciNet  Google Scholar 

  18. Olver, P. J.: Conservation laws in elasticity. III. Planar linear anisotropic elastostatics. Arch. Rational Mech. Anal. 102, 167–181 (1988).

    MathSciNet  MATH  Google Scholar 

  19. Caviglia, G., Morro, A.: Inhomogeneous Waves in Solids and Fluids. Singapore: WSPC 1992.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Caviglia, G., Morro, A. (1993). Conservation Laws in Dissipative Solids. In: Ibragimov, N.H., Torrisi, M., Valenti, A. (eds) Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2050-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2050-0_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4908-5

  • Online ISBN: 978-94-011-2050-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics