Skip to main content

Nonhomogeneous quasilinear hyperbolic systems: Initial and boundary value problem

  • Conference paper
  • First Online:
Calculus of Variations and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1340))

  • 928 Accesses

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 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight 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. W. Allard, The first variation of a varifold, Ann. of Math. 95 (1972), 417–491.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Courant, K.O. Friedrichs and H. Lewy, Über di Partilellen Differenzengleichungen der Mathematischen Physik, Math. Ann. 100 (1928), 32–74.

    Article  MathSciNet  MATH  Google Scholar 

  3. C.M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Mathematics J. 31 (1982), 471–491.

    Article  MathSciNet  MATH  Google Scholar 

  4. R.J. Di Perna, Global solutions to a class of nonlinear hyperbolic systems of equations, Comm. Pure and Appl. Math. 26 (1973), 1–28.

    Article  MathSciNet  Google Scholar 

  5. D. Fujiwara and S. Takakuwa, A varifold solution to the nonlinear equation of motion of a vibrating membrane, preprint Dept. of Mathematics, Tokyo Institute of Technology.

    Google Scholar 

  6. J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure and Appl. Math. 18 (1965), 697–715.

    Article  MathSciNet  MATH  Google Scholar 

  7. E. Giusti, Minimal surfaces and functions of bounded variation, Notes on Pure Mathematics 10 (1977), Australian National University, Canberra.

    MATH  Google Scholar 

  8. L. Hsiao and P. Marcati, A nonhomogeneous quasilinear hyperbolic system arising in chemical engineering, submitted.

    Google Scholar 

  9. P.D. Lax, Hyperbolic systems of conservation law, Comm. Pure and Appl. Math. 10 (1957), 537–566.

    Article  MathSciNet  MATH  Google Scholar 

  10. T.-P. Liu, Quasilinear hyperbolic systems, Comm. Math. Phys. 68 (1979), 141–172.

    Article  MathSciNet  MATH  Google Scholar 

  11. T.P. Liu, Hyperbolic conservation laws with relaxation and damping, Proceedings Int. Conf. L’Aquila 1986.

    Google Scholar 

  12. T.-P. Liu, The free piston problem for gas dynamics, J. Diff. Eqns 30 (1978), 175–191.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Miranda, Distribuzioni aventi derivate misure ed insiemi di perimetro localmente finito, Ann. Scuola Norm. Sup. Pisa 18 (1964), 27–56.

    MathSciNet  MATH  Google Scholar 

  14. M. Miranda, Comportamento delle successioni convergenti di frontiere minimali, Rend. Sem. Mat. Univ. Padova 38 (1967), 238–257.

    MathSciNet  MATH  Google Scholar 

  15. T. Nishida and J.A. Smoller, Mixed problems for nonlinear conservation laws, J. Diff. Eqns 23 (1977), 244–269.

    Article  MathSciNet  MATH  Google Scholar 

  16. J.A. Smoller, Schock waves and reaction-diffusion equations, Grundlehren der mathematischen Wissenschaften 258, Springer-Verlag, New York-Heidelberg-Berlin 1983.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Stefan Hildebrandt David Kinderlehrer Mario Miranda

Additional information

Dedicated to Hans Lewy

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Marcati, P. (1988). Nonhomogeneous quasilinear hyperbolic systems: Initial and boundary value problem. In: Hildebrandt, S., Kinderlehrer, D., Miranda, M. (eds) Calculus of Variations and Partial Differential Equations. Lecture Notes in Mathematics, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082896

Download citation

  • DOI: https://doi.org/10.1007/BFb0082896

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50119-0

  • Online ISBN: 978-3-540-45932-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics