The Random Choice Method

  • Constantine M. Dafermos
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 325)


The endeavor of solving the initial-value problem for the scalar conservation law, in Chapter VI, owes its spectacular success to the L 1 -contraction property, which applies not only to the solutions themselves but even to their approximations by means of vanishing viscosity, layering, relaxation, etc. For systems, however, the situation is different: L 1-contraction no longer applies; in its place, L 1-Lipschitz continuity will eventually be established, in Chapter XIV, albeit under substantial restrictions on the initial data. Furthermore, at the time of this writing, the requisite stability estimates have been established solely in the context of highly specialized approximating schemes that employ as building blocks the solution of the Riemann problem.


Rarefaction Wave Riemann Problem Wave Interaction Characteristic Family Random Choice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Constantine M. Dafermos
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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