Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system |
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Authors: | Peipei Shang Zhiqiang Wang |
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Institution: | a INRIA Paris-Rocquencourt Centre, France b School of Mathematical Sciences, Fudan University, Shanghai 200433, China c Université Pierre et Marie Curie-Paris 6, UMR 7598 Laboratoire Jacques-Louis Lions, 75005 Paris, France |
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Abstract: | In this paper, we study a scalar conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. As a generalization of Coron et al. (2010) 14], the velocity function possesses both the local and nonlocal character. We prove the existence and uniqueness of the weak solution to the Cauchy problem with initial and boundary data in L∞. We also obtain the stability (continuous dependence) of both the solution and the out-flux with respect to the initial and boundary data. Finally, we prove the existence of an optimal control that minimizes, in the Lp-sense with 1?p?∞, the difference between the actual out-flux and a forecast demand over a fixed time period. |
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Keywords: | 35L65 49J20 93C20 |
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