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Weak Measure-Valued Solutions to a Nonlinear Conservation Law Modeling a Highly Re-entrant Manufacturing System


Abstract The main part of this work establishes existence, uniqueness and regularity properties of measure-valued solutions of a nonlinear hyperbolic conservation law with non-local velocities. Major challenges stem from in- and out-fluxes containing nonzero pure-point parts which cause discontinuities of the velocities. This part is preceded, and motivated, by an extended study which proves that an associated optimal control problem has no optimal $L^1$-solutions that are supported on short time intervals.

The hyperbolic conservation law considered here is a well-established model for a highly re-entrant semiconductor manufacturing system. Prior work established well-posedness for $L^1$-controls and states, and existence of optimal solutions fo... (more)
Created Date 2019
Contributor Gong, Xiaoqian (Author) / Kawski, Matthias (Advisor) / Kaliszewski, Steven (Committee member) / Motsch, Sebastien (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Subject Mathematics / Nonlinear Hyperbolic Conservation Law / Optimal Control / Supply Chain / Weak Measure-Valued Solution
Type Doctoral Dissertation
Extent 120 pages
Language English
Copyright
Note Doctoral Dissertation Applied Mathematics 2019
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis