Discontinuous Initial Value Problems and Asymptotic Expansion of Steady-State Solutions (Classic Reprint)

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Excerpt from Discontinuous Initial Value Problems and Asymptotic Expansion of Steady-State Solutions

Discontinuous solutions of hyperbolic partial differential equations have often been treated in the mathematical literature. The earlier treat ments dealt mainly with second order equations (see e.g. [l], Recently R. Courant and p.d. Lax[3] extended the theory to first order linear hyper bolic systems and proved an existence theorem for discontinuous solutions of initial value problems. In Part I of this paper we generalize the theory of Courant and Lax in two respects. First we consider more general equations. This generalization is not without interest for it permits the inclusion of some important equations of mathematical physics: $ Second we consider initial boundary value problems rather than pure initial value problems.

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