A Semi-linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton–Jacobi–Bellman Type and Applications to Optimal Control

Journal Article · Sat Aug 15 00:00:00 EDT 2015 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-014-9270-4· OSTI ID:22469891

Addona, Davide ^[1]

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1. Università degli Studi di Milano Bicocca, (MILANO BICOCCA) Dipartimento di Matematica (Italy)

We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton–Jacobi–Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the value function of the controlled equation and that the feedback law is verified.

• OSTI ID: 22469891
• Journal Information: Applied Mathematics and Optimization, Vol. 72, Issue 1; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
CAUCHY PROBLEM
DIFFERENTIAL EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL
STOCHASTIC PROCESSES