AN ORDERING PRINCIPLE AND GENERALIZED SOLUTIONS OF CERTAIN QUASI-LINEAR PARTIAL DIFFERENTIAL EQUATIONS

摘要

In this paper is set forth a simple unifying principle governing the solutions of continuous and discontinuous initial value problems for partial differential equations of the form (1.1) ut + (F(u))x = 0 with convex, or concave, F(u). This principle provides easy, elementary means both to construct these solutions and also to demonstrate their uniqueness and other properties.