Dissertation
A Cauchy-Kovalevskaya theorem for the mean field games system
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2021
DOI:
https://doi.org/10.17918/00000793
Abstract
The mean field games system of partial differential equations is comprised of a backward parabolic Hamilton-Jacobi-Bellman equation and a forward parabolic Fokker-Planck equation. We prove an abstract Cauchy-Kovalevskaya theorem for forward-backward systems, which we then apply to prove existence of solutions to the mean field games system. We then show that the zero diffusion limit may be taken, proving that solutions of the first-order mean field games system are the zero diffusion limit of the solutions of the parabolic mean field games system.
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Details
- Title
- A Cauchy-Kovalevskaya theorem for the mean field games system
- Creators
- Benjamin T. Irwin
- Contributors
- David M. Ambrose (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- v, 40 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991015241382704721