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  • Viability for locally monotone evolution inclusions and lower semicontinuous solutions of Hamilton–Jacobi–Bellman equations in infinite dimensions
Title: Viability for locally monotone evolution inclusions and lower semicontinuous solutions of Hamilton–Jacobi–Bellman equations in infinite dimensions
We establish necessary and sufficient conditions for viability of evolution inclusions with locally monotone operators in the sense of Liu and Röckner [J. Funct. Anal., 259 (2010), pp. 2902-2922]. This allows us to prove wellposedness of lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations associated to the optimal control of evolution inclusions. Thereby, we generalize results in Bayraktar and Keller [J. Funct. Anal., 275 (2018), pp. 2096-2161] on Hamilton-Jacobi equations in infinite dimensions with monotone operators in several ways. First, we permit locally monotone operators. This extends the applicability of our theory to a wider class of equations such as Burgers' equations, reaction-diffusion equations, and 2D Navier-Stokes equations. Second, our results apply to optimal control problems with state constraints. Third, we have uniqueness of viscosity solutions. Our results on viability and lower semicontinuous solutions are new even in the case of monotone operators.  more » « less
Award ID(s):
2106077
PAR ID:
10651771
Author(s) / Creator(s):
;
Publisher / Repository:
EDP Sciences
Date Published:
Journal Name:
ESAIM: Control, Optimisation and Calculus of Variations
Volume:
31
ISSN:
1292-8119
Page Range / eLocation ID:
4
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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