Annali di Matematica Pura ed Applicata

, Volume 105, Issue 1, pp 281–294

Weak solutions of nonlinear hyperbolic conservation laws

  • P. Ramankutty

DOI: 10.1007/BF02414934

Cite this article as:
Ramankutty, P. Annali di Matematica (1975) 105: 281. doi:10.1007/BF02414934


A weak solution of the conservation law ut+j(ux)=0 is a locally Lipschitzian function u which satisfies the equation almost everywhere. We treat a boundary value problem and also a mixed initial-boundary value problem associated with the equation where the initial and boundary data are convex functions. The convexity hypothesis makes it possible to apply the Fenchel theory of conjugate convex functions to the problem. This leads to a construction of solutions rather than to a proof of their existence; the solutions so constructed turn out to be stable.

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • P. Ramankutty
    • 1
  1. 1.AucklandNew Zealand

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