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Journal of Control Science and Engineering
Volume 2010, Article ID 982369, 10 pages
Research Article

On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms

1Dipartimento di Ingegneria Elettronica e Ingegneria Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, 84084 Fisciano, Italy
2Department of Differential Equations, Dnipropetrovsk National University, Gagarin Avenue, 72, 49010 Dnipropetrovsk, Ukraine

Received 9 September 2010; Accepted 18 December 2010

Academic Editor: Yoshito Ohta

Copyright © 2010 Ciro D'Apice et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study one class of nonlinear fluid dynamic models with impulse source terms. The model consists of a system of two hyperbolic conservation laws: a nonlinear conservation law for the goods density and a linear evolution equation for the processing rate. We consider the case when influx-rates in the second equation take the form of impulse functions. Using the vanishing viscosity method and the so-called principle of fictitious controls, we show that entropy solutions to the original Cauchy problem can be approximated by optimal solutions of special optimization problems.