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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.

Linked References

  1. A. Bressan, Hyperbolic Systems of Conservation Laws—The One-dimensional Cauchy Problem, Oxford University Press, Oxford, UK, 2000.
  2. S. Kruzhkov, “First-order quasilinear equations in several independent variables,” Mathematics of the USSR-Sbornik, vol. 10, pp. 217–243, 1970. View at Google Scholar
  3. P. D. Lax, Hyperbolic System of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, Pa, USA, 1973.
  4. C. D'apice and R. Manzo, “A fluid dynamic model for supply chains,” Networks and Heterogeneous Media, vol. 1, no. 3, pp. 379–398, 2006. View at Google Scholar
  5. E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Boston, Mass, USA, 1984.
  6. M. Garavello and B. Piccoli, Traffic Flow on Networks, vol. 1 of AIMS Series on Applied Mathematics, 2006.
  7. G. A. Chechkin and A. Yu. Goritsky, “S. N. Kruzhkov’s lectures on first-order quasilinear PDEs,” Analytical and Numerical Aspects of PDEs, pp. 1–67, 2010. View at Google Scholar
  8. S. Ulbrich, Optimal Control of Nonlinear Hyperbolic Conservation Laws with Source Terms, Fakultät für Mathematik,Technische Universität München, 2002.
  9. D. Armbruster, D. Marthaler, and C. Ringhofer, “Kinetic and fluid model hierarchies for supply chains,” SIAM Journal on Multiscale Modeling and Simulation, vol. 2, pp. 43–61, 2004. View at Google Scholar
  10. S. Göttlich, M. Herty, and A. Klar, “Modelling and optimization of supply chains on complex networks,” Communications in Mathematical Sciences, vol. 4, no. 2, pp. 315–330, 2006. View at Google Scholar
  11. C. Kirchner, M. Herty, S. Göttlich, and A. Klar, “Optimal control for continuous supply network models,” Networks and Heterogeneous Media, vol. 1, no. 4, pp. 675–688, 2006. View at Google Scholar
  12. J. L. Lions, Some Methods of Solving Non-Linear Boundary Value Problems, Dunod-Gauthier-Villars, Paris, France, 1969.
  13. V. A. Solonnikov, “A priori estimates for equations of second order parabolic type,” Trudy Matematicheskogo Instituta imeni V.A. Steklova, vol. 70, pp. 133–212, 1960. View at Google Scholar