Skip to main content
SpringerLink
Log in

Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

The paper discusses the long time behavior of BV solutions to the Cauchy problem for hyperbolic systems of balance laws with partial dissipation, when the relaxed system is adiabatic.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. There is also extensive treatment of these problems in the realm of classical solutions. For a recent survey and references, see [10].

References

  1. Cattaneo, C.: Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena 3, 83–101 (1949)

    MathSciNet  MATH  Google Scholar 

  2. Dafermos, C.M.: Hyperbolic systems of balance laws with weak dissipation. J. Hyperbolic Differ. Equ. 3, 507–527 (2006)

    MathSciNet  MATH  Google Scholar 

  3. Dafermos, C.M.: Hyperbolic systems of balance laws with weak dissipation II. J. Hyperbolic Differ. Equ. 10, 173–179 (2013)

    Article  MathSciNet  Google Scholar 

  4. Dafermos, C.M.: BV solutions for hyperbolic systems of balance laws with relaxation. J. Differ. Equ. 255, 2521–2533 (2013)

    Article  MathSciNet  Google Scholar 

  5. Dafermos, C.M.: BV solutions of hyperbolic balance laws with relaxation in the absence of conserved quantities. SIAM J. Math. Anal. 46, 4014–4034 (2014)

    Article  MathSciNet  Google Scholar 

  6. Dafermos, C.M.: Asymptotic behavior of BV solutions to hyperbolic systems of balance laws with relaxation. J. Hyperbolic Differ. Equ. 12, 277–292 (2015)

    Article  MathSciNet  Google Scholar 

  7. Dafermos, C.M.: Hyperbolic balance laws with relaxation. Discrete Contin. Dyn. Syst. Ser. A 36, 4271–4285 (2016a)

    Article  MathSciNet  Google Scholar 

  8. Dafermos, C.M.: Hyperbolic Conservation Laws in Continuum Physics, 4th edn. Springer, Heidelberg (2016b)

    MATH  Google Scholar 

  9. Ruggeri, T., Serre, D.: Stability of constant equilibrium state for dissipative balance laws systems with a convex entropy. Quart. Appl. Math. 62, 163–179 (2004)

    Article  MathSciNet  Google Scholar 

  10. Xu, J., Kawashima, S.: Existence and time decay estimates for hyperbolic systems with dissipation. Adv. Math. 46, 321–330 (2017). (China)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Constantine M. Dafermos

Authors
  1. Constantine M. Dafermos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Constantine M. Dafermos.

Additional information

Communicated by S. Rionero.

Dedicated with affection to Tommaso Ruggeri on his seventieth birthday.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dafermos, C.M. Hyperbolic balance laws with dissipative source relaxing to adiabatic conservation laws. Ricerche mat 67, 755–764 (2018). https://doi.org/10.1007/s11587-017-0338-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-017-0338-8

Keywords

Mathematics Subject Classification

Search

Navigation