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.
Download count: 0
- Partial requirement for: Ph.D., Arizona State University, 2019Note typethesis
- Includes bibliographical references (pages 95-96)Note typebibliography
- Field of study: Applied mathematics