On Discontinuous Initial Value Problems for Certain Non-Linear Partial Differential Equations

摘要

The partial differential equations discussed in this paper are of the from (*) ut + (F u)) O with F u) continuously differentiable and conver. The initial data admitted are bounded, measurable functions on the x-axis vanishing for x<0. The solutions sought are functions with such orescribed data which are defined in the entire upper halfplane and satiafy (*) in a suitable integral sense.