Boundary value problems for stationary Hamilton-Jacobi and Bellman equations

1994 ◽  
pp. 456-465
Author(s):  
Victor P. Maslov ◽  
Sergei N. Samborski
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Bellman Equations

scholarly journals Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators

2019 ◽  
Vol 65 ◽  
pp. 425-444 ◽  
Author(s):  
M. Lauriere ◽  
Z. Li ◽  
L. Mertz ◽  
J. Wylie ◽  
S. Zuo
Keyword(s):  
Optimal Control ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Dirichlet Boundary Conditions ◽  
Kolmogorov Equation ◽  
Bellman Equations ◽  
Random Forcing ◽  
Free Boundary Value Problems

We consider the optimal stopping and optimal control problems related to stochastic variational inequalities modeling elasto-plastic oscillators subject to random forcing. We formally derive the corresponding free boundary value problems and Hamilton-Jacobi-Bellman equations which belong to a class of nonlinear partial of differential equations with nonlocal Dirichlet boundary conditions. Then, we focus on solving numerically these equations by employing a combination of Howard’s algorithm and the numerical approach [A backward Kolmogorov equation approach to compute means, moments and correlations of non-smooth stochastic dynamical systems; Mertz, Stadler, Wylie; 2017] for this type of boundary conditions. Numerical experiments are given.

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