Abstract
We consider Hamilton–Jacobi equations which characterize optimal controlled partial differential equations of the following types: the Allen–Cahn equation, the Cahn–Hilliard equation, a nonlinear Fokker–Planck equation, and a Vlasov–Fokker–Planck equation. In each of the examples, the optimal control problem and its associated cost functional can be derived as limit from a microscopically defined stochastic system, using the probabilistic theory of large deviation. The physical context here makes it natural to derive a free energy inequality, which is very useful in proving the well-posedness of the Hamilton–Jacobi equation. The article is written using informal arguments. Rigorous results will appear elsewhere.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
