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2010, Volume 14, Issue 4: 1337-1359. Doi: 10.3934/dcdsb.2010.14.1337
This issue Previous Article On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions Next Article On the relevance of the dam break problem in the context of nonlinear shallow water equations

Analysis of a conservation law modeling a highly re-entrant manufacturing system

  • 1.

    Institut universitaire de France and Université Pierre et Marie Curie-Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, Paris, F-75005

  • 2.

    Arizona State University, Tempe, Arizona 85287-1804

  • 3.

    Fudan University and Université Pierre et Marie Curie-Paris VI, UMR 7598, Laboratoire Jacques-Louis Lions, 4, place Jussieu, Paris, F-75005

Received:  June 30, 2009
Revised:  February 28, 2010
Published:  May 2010
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    Abstract
  • This article studies a hyperbolic conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. Characteristic features are the nonlocal character of the velocity and that the influx and outflux constitute the control and output signal, respectively. We prove the existence and uniqueness of solutions for $L^1$-data, and study their regularity properties. We also prove the existence of optimal controls that minimizes in the $L^2$-sense the mismatch between the actual and a desired output signal. Finally, the time-optimal control for a step between equilibrium states is identified and proven to be optimal.
    Mathematics Subject Classification: Primary: 35L65, 49J20, 93C20.

    Citation:
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