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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 3, 2001, pp. 599–615
DOI: 10.4171/ZAA/1034

Published online: 2001-09-30

Entropy Solution for a Hyperbolic Equation

Sévérine Bernard[1]

(1) Université des Antilles et de la Guyane, Pointe-A-Pitre, Guadeloupe (French)

Nonlinear hyperbolic systems of conservation laws play a central role in Science and Engineering, and their mathematical theory as well as their numerical approximation have made recent significative progress. This paper deals with the existence and uniqueness of an entropy solution of the Cauchy problem for the quasi-linear equation $u-t + a(f(u))_x = 0$ in one space dimension, where $a$ is a non-smooth coefficient.

Keywords: Conservation laws, discontinuous coefficients, product of distributions, entropy solutions

Bernard Sévérine: Entropy Solution for a Hyperbolic Equation. Z. Anal. Anwend. 20 (2001), 599-615. doi: 10.4171/ZAA/1034