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)
|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|
|Note||Doctoral Dissertation Applied Mathematics 2019|
|Collaborating Institutions||Graduate College / ASU Library|
|Additional Formats||MODS / OAI Dublin Core / RIS|