Skip to main content
SpringerLink
Log in

Wave features of a hodograph-like transformation for quasilinear hyperbolic systems

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

We study the properties of a variables transformation for a 2×2 quasilinear hyperbolic nonhomogeneous system of first order, related to wave propagation. The considered variables transformation transforms characteristic curves of the original system, into characteristic curves of the transformed system. We make use of this property to study the propagation of weak discontinuities (acceleration waves) compatible with the quasilinear system (1.1). Finally a special class of rate-type media is considered and asymptotic solutions are investigated.

Sommario

Si studiano le proprietà di una trasformazione di variabili per un sistema quasilineare iperbolico del primo ordine non omogeneo. La trasformazione considerata trasforma curve caratteristiche del sistema originale in curve caratteristiche del sistema trasformato. Utilizzando queste proprietà si studia la propagazione delle onde di discontinuità (onde di accelerazione) compatibile con il sistema quasilineare iperbolico considerato e si cercano soluzioni asintotiche.

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

References

  1. D. Fusco and N. Manganaro,Prominent features of a variable transformation for a class of quasilinear hyperbolic systems of first order. InNonlinear Wave Motion, A. Jeffrey ed., Longman, Harlow, U.K.

  2. B. Seymour and E. Varley,Exact solutions for large amplitude waves in dispersive and dissipative systems. Studies Appl. Math.72, 241–262 (1985).

    Google Scholar 

  3. G. Boillat,La Propagation des Ondes. Gauthier-Villars, Paris 1965.

    Google Scholar 

  4. A. Jeffrey,Quasilinear Hyperbolic Systems and Waves. Pitman, London 1976.

    Google Scholar 

  5. G. Boillat and T. Ruggeri,On the evolution law of weak discontinuities for hyperbolic quasilinear systems. Wave Motion1, 149–152 (1979).

    Google Scholar 

  6. G. W. Bluman and J. D. Cole,Similarity Methods for Differential Equations. Springer, Berlin 1974.

    Google Scholar 

  7. W. F. Ames,Nonlinear Partial Differential Equations in Engineering. Vol. II, Academic Press, New York 1972.

    Google Scholar 

  8. Y. Choquet-Bruaht,Ondes asymptotiques et approaches pour des systems d'equations aux derivees partialles non lineaires. J. Math. Pure Appl.48, 117–158 (1969).

    Google Scholar 

  9. G. Boillat,Ondes asymptotiques non lineaires. Ann. Mat. Pura ed Applicata IV,111, 31–44 (1976).

    Google Scholar 

  10. R. Courant and D. Hilbert,Methods of Mathematical Physics. Vol. II, Interscience Publ., New York 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica dell'Università di Messina, Salita Sperone 31, Contrada Papardo, 98166, Sant'Agata, Messina, Italy

    Carmela Curró

Authors
  1. Carmela Curró
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the C.N.R. through the G.N.F.M. and partially under contract No. 88. 01855.01.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Curró, C. Wave features of a hodograph-like transformation for quasilinear hyperbolic systems. Z. angew. Math. Phys. 41, 38–50 (1990). https://doi.org/10.1007/BF00946073

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00946073

Keywords

Search

Navigation