Uniqueness Result for the Generalized Entropy Solutions to the Cauchy Problem for First-Order Partial Differential-Functional Equations

Abstract

We prove a theorem on differential-functional inequalities in the Carathéodory sense. The proof is based on the faèt that we can solve a linear differential equation with first-order partial derivatives. We use also an integral Volterra-type inequality. We obtain a theorem on the uniqueness of generalized entropy solutions to the initial-value problem for non-linear partial differentialfunctional equations of the first order.