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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 3, 1994, pp. 477–491
DOI: 10.4171/ZAA/500

Published online: 1994-09-30

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

Zdzisław Kamont[1] and H. Leszczyński[2]

(1) University of Gdansk, Poland
(2) University of Gdansk, Poland

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.

Keywords: Integral inequalities, method of regularization, Volterra condition, characteristic problem

Kamont Zdzisław, Leszczyński H.: Uniqueness Result for the Generalized Entropy Solutions to the Cauchy Problem for First-Order Partial Differential-Functional Equations. Z. Anal. Anwend. 13 (1994), 477-491. doi: 10.4171/ZAA/500