Archive for Rational Mechanics and Analysis

, Volume 156, Issue 2, pp 89–119 | Cite as

Global Continuous Riemann Solver for Nonlinear Elasticity

  • Jean-Marc Mercier
  • Benedetto Piccoli


We consider in this paper an isothermal model of nonlinear elasticity. This model is described by two conservation laws that define a problem of mixed type, both elliptic and hyperbolic. We restrict ourselves to the linearly degenerate case, and consider Riemann data that lies in the hyperbolic regions. The lack of uniqueness of the Riemann problem is solved by the introduction of a so-called kinetic relation, used to narrow the set of admissible subsonic phase transitions. In this situation, we consider the Riemann problem for any data lying in the hyperbolic region, using either explicit computations or geometric arguments. This construction allows us to give sufficient conditions on the kinetic relation in order that the generated Riemann solver possesses properties of uniqueness, globality, and continuous dependence on the initial data in the L 1 distance.


Phase Transition Initial Data Mixed Type Isothermal Model Explicit Computation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jean-Marc Mercier
    • 1
  • Benedetto Piccoli
    • 2
  1. 1.SISSA¶Via Beirut 2–4¶34014 Trieste¶Italy¶E-mail: jeanmarc.mercier@free.frFR
  2. 2.DIIMA, Universitá di Salerno¶Via Ponte Don Melillo¶84084 Fisciano (SA)¶Italy¶E-mail: piccoli@sissa.itIT

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