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

1994; European Mathematical Society; Volume: 13; Issue: 3 Linguagem: Inglês

10.4171/zaa/500

1661-4534

Zdzisław Kamont, Henryk Leszczyński,

advanced mathematical theories

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.