Abstract
The optimal control of a distributed parameter system is connected to the solution of the corresponding Hamilton-Jacobi equation. This is a first-order equation in infinite dimensions with discontinuous coefficients. We study the Hamilton-Jacobi equation of a system governed either by a “semilinear” or by a “monotone” dynamics, replacing the unbounded terms of this equation by their Yosida approximations. We prove convergence of the approximate solutions to the value function of the original problem, by using the uniqueness result for viscosity solutions. Examples and applications are included.
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