Nonlinear conservation law model for production network considering yield loss
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Authors
Tanmay Sarkar
- Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036, India.
S. Sundar
- Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036, India.
Abstract
A mathematical model describing yield loss in a production network has been introduced. Mathematical
properties of the continuum model are discussed. Existence, uniqueness and stability of the solution are
demonstrated through weak formulation and entropy criteria. Front tracking method is implemented to
construct approximate solutions. Estimates of the solutions are also provided.
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ISRP Style
Tanmay Sarkar, S. Sundar, Nonlinear conservation law model for production network considering yield loss, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 3, 205--217
AMA Style
Sarkar Tanmay, Sundar S., Nonlinear conservation law model for production network considering yield loss. J. Nonlinear Sci. Appl. (2014); 7(3):205--217
Chicago/Turabian Style
Sarkar, Tanmay, Sundar, S.. "Nonlinear conservation law model for production network considering yield loss." Journal of Nonlinear Sciences and Applications, 7, no. 3 (2014): 205--217
Keywords
- Production system
- conservation laws
- yield loss
- front tracking.
MSC
References
-
[1]
D. Armbruster, P. Degond, C. Ringhofer, A model for the dynamic of large queuing networks and supply chains, SIAM J. Appl. Math., 66 (2006), 896–920.
-
[2]
A. Bressan, Hyperbolic Systems of conservation Laws, Oxford University Press, Oxford (2000)
-
[3]
C. M. Dafermos, Polygonal Approximations of Solutions of the Inital Value Problem for a Conservation Law, J. Math. Anal. Appl., 38 (1972), 33–41.
-
[4]
C. M. Dafermos, Generalized Characteristics and the Structure of Solutions of Hyperbolic Conservation Law, Indiana Univ. Math. J., 26 (1977), 1097–1119.
-
[5]
C. D’Apice, R. Manzo, A Fluid Model for supply Chains, Netw. Heterog. Media, 1 (2006), 379–398.
-
[6]
C. D’Apice, S. Göttlich, M. Herty, B. Piccoli, Modeling, Simulation and Optimization of Supply Chains, A continuous Approach, SIAM (2010)
-
[7]
S. Göttlich, M. Herty, A. Klar , Network models for supply chains , Comm. Math. Sci., 3 (2005), 545–559.
-
[8]
S. Göttlich, M. Herty, A. Klar, Modelling and optimization of supply chains on complex network, Comm. Math. Sci., 4 (2006), 315–330.
-
[9]
M. Herty, A. Klar, B. Piccoli , Existence of solutions for Supply Chain Models based on Partial Differential Equations, SIAM J. Math. Anal., 39 (2007), 160–173.
-
[10]
H. Holden, N. H. Risebro , Front Tracking for hyperbolic Conservation Laws, Springer Verlag, New York, Berlin, Heidelberg (2002)
-
[11]
Y. Kan, T. Tang, Z. Teng, On the Piecewise Smooth Solutions to non-homogeneous Scalar Conservation Laws, J. Differential Equations, 175 (2001), 27–50.
-
[12]
C. Kirchner, M. Herty, S. Göttlich, A. Klar, Optimal Control for Continuous Supply Network Models, Netw. Heterog. Media, 1 (2006), 675–688.
-
[13]
S. N. Kruzhkov, First Order Quasilinear Equations in Several Independent Variables, Math. USSR-Sb., 10 (1970), 217–243.
-
[14]
R. J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, (2008)
-
[15]
G. F. Newell, A simplified theory of kinematic waves in highway traffic, Transportation Res., 27B (1993), 281– 313.
-
[16]
T. Sarkar, S. Sundar , Conservation law model of serial supply chain network incorporating various velocity forms, Int. J. Appl. Math., 26 (2013), 363–378.
-
[17]
T. Sarkar, S. Sundar, On existence and stability analysis of a nonlinear conservation law model appearing in production system, Nonlinear Stud., 21 (2014), 339–347.
-
[18]
A. H. Soliman, M. A. Barakat, Uniformly normal structure and uniformly generalized Lipschitzian semigroups, J. Nonlinear Sci. Appl., 5 (2012), 379-388.
-
[19]
S. Sun, M. Dong, Continuum modeling of Supply Chain networks using discontinuous Galerkin methods, Comput. Methods Appl. Mech. Engg., 197 (2008), 1204–1218.