Skip to main content
SpringerLink
Log in
Book cover

Hyperbolic Conservation Laws in Continuum Physics pp 19–35Cite as

Introduction to Continuum Physics

  • Chapter

  • 733 Accesses

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 325))

Abstract

In Continuum Physics, material bodies are modelled as continuous media whose motion and equilibrium is governed by balance laws and constitutive relations.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. Truesdell, C.A. and R.A. Toupin: The Classical Field Theories. Handbuch der Physik, Vol. III/1. Berlin: Springer, 1960.

    Google Scholar 

  2. Truesdell, C.A. and W. Noll: The Non-Linear Field Theories of - Mechanics. Handbuch der Physik, Vol. 111/3. Berlin: Springer, 1965.

    Google Scholar 

  3. Gurtin, M.E.: An Introduction to Continuum Mechanics. New York: Academic Press, 1981.

    MATH  Google Scholar 

  4. Silhavÿ, M.: The Mechanics and Thermodynamic’s of Continuous Media. Berlin: Springer, 1997.

    MATH  Google Scholar 

  5. Ciarlet, P.G.: Mathematical Elasticity. Amsterdam: North-Holland, 1988.

    MATH  Google Scholar 

  6. Hanyga, A.: Mathematical Theory of Non-Linear Elasticity. Warszawa: PWN, 1985.

    Google Scholar 

  7. Marsden, J.E. and T.J.R. Hughes: Mathematical Foundations of Elasticity. Englewood Cliffs: Prentice-Hall, 1983.

    MATH  Google Scholar 

  8. Wang, C.C. and C. Truesdell: Introduction to Rational Elasticity. Leyden: Noordhoff, 1973.

    MATH  Google Scholar 

  9. Antman, S.S.: Nonlinear Problems of Elasticity. New York: Springer, 1995.

    Book  MATH  Google Scholar 

  10. Dafermos, C.M.: Equivalence of referential and spatial field equations in continuum physics. Notes Num. Fluid Mech. 43 (1993), 179–183.

    MathSciNet  Google Scholar 

  11. Wagner, D.H.: Conservation laws, coordinate transformations, and differential forms. Hyperbolic Problems: Theory, Numerics, Applications, pp. 471–477, eds. J. Glimm, M.J. Graham, J.W. Grove and B.J. Plohr. Singapore: World Scientific, 1996.

    Google Scholar 

  12. Wagner, D.H.: Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions. J. Diff. Eqs. 68 (1987), 118–136.

    Article  MATH  Google Scholar 

  13. Euler, L.: Principes généraux du mouvement des fluides. Mém. Acad. Sci. Berlin 11 (1755), 274–3I5.

    Google Scholar 

  14. Euler, L.: Supplément aux recherches sur la propagation du son. Mém. Acad. Sci. Berlin 15 (1759), 210–240.

    Google Scholar 

  15. Cauchy, A.-L.: Sur les relations qui existent dans l’état d’équilibre d’un corps solide ou fluide, entre les pressions ou tensions et les forces accélératrices. Exercises de Mathématiques 2 (1827), 108–111.

    Google Scholar 

  16. Cauchy, A.-L.: Sur l’équilibre et le mouvement intérieur des corps considérés comme des masses continues. Exercises de Mathématiques 4 (1829), 293–319.

    MATH  Google Scholar 

  17. Kirchhoff, G.: Ueber den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung. Ann. Physik 134 (1868), 177–193.

    Article  Google Scholar 

  18. Clausius, R.: Über einer veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie. Ann. Physik 93 (1854), 481–506.

    Article  Google Scholar 

  19. Duhem, P.: Recherches sur l’hydrodynamique. Ann. Toulouse 3 (1901), 315–377.

    Article  MathSciNet  MATH  Google Scholar 

  20. Coleman, B.D. and W. Noll: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rational Mech. Anal. 13 (1963), 167–178.

    MathSciNet  MATH  Google Scholar 

  21. Coleman, B.D. and V.J. Mizel: Existence of caloric equations of state in thermodynamics. J. Chem. Phys. 40 (1964), 1116–1125.

    Article  MathSciNet  Google Scholar 

  22. Cauchy, A.-L.: Sur l’équilibre et le mouvement intérieur des corps considérés comme des masses continues. Exercises de Mathématiques 4 (1829), 293–319.

    Google Scholar 

  23. Poisson, S.D.: Mémoire sur les équations générales de l’équilibre et du mouvement des corps élastiques et des fluides. J. Ecole Polytechnique, 13 (1831), 1–174.

    Google Scholar 

  24. Cosserat, E.: Théorie des Corps Déf trmables. Paris: Hermann, 1909.

    Google Scholar 

  25. Rivlin, R.S. and J.L. Ericksen: Stress-deformation relations for isotropic materials. J. Rational Mech. Anal. 4 (1955), 323–425.

    MathSciNet  MATH  Google Scholar 

  26. Noll, W.: A mathematical theory of the mechanical behavior of continuous media. Arch. Rational Mech. Anal. 2 (1958), 197–226.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Constantine M. Dafermos

Authors
  1. Constantine M. Dafermos
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Dafermos, C.M. (2000). Introduction to Continuum Physics. In: Hyperbolic Conservation Laws in Continuum Physics. Grundlehren der mathematischen Wissenschaften, vol 325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-22019-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-22019-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-22021-4

  • Online ISBN: 978-3-662-22019-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation