Vol. 42, No. 1, 1972

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ISSN: 0030-8730
Shock sets for first order nonlinear hyperbolic equations

Donald Pollard Ballou

Vol. 42 (1972), No. 1, 17–26
Abstract

This paper studies those values u which can be reached from u0 across a shock or contact discontinuity which may arise in weak solutions to the Cauchy problem

∂u-  ∂F(u)-
∂t +  ∂x   = 0

         0
u(0,x) = u (x),

where it is not assumed that F′′ > 0. A condition which guarantees uniqueness is used to define a set lS(u0) consisting of such values u. The close relationship between lS(u0) and the geometry of F(u) is examined, and properties of this set are derived which give information about the interaction of curves of discontinuity.

Mathematical Subject Classification 2000
Primary: 35L65
Milestones
Received: 2 March 1971
Published: 1 July 1972
Authors
Donald Pollard Ballou