Microscopic derivations of several Hamilton–Jacobi equations in infinite dimensions, and large deviation of stochastic systems
نویسندگان
چکیده
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 aVlasov–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. 2005 Elsevier Ltd. All rights reserved.
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