In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application to PDEs systems concerns the behavior of optimal time and of the associated optimal controls for parabolic equations with highly oscillating coefficients, as we encounter in homogenization theory. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the solutions of the time optimal control problems for the systems with oscillating coefficients converge, in the usual norms, to the solution of the corresponding problem for the homogenized system. In order to prove our main theorem, we provide several new results, which could be of a broader interest, on time and norm optimal control problems.
Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence
A Nonparametric, Mixed Effect, Maximum Likelihood Estimator for the Distribution of Random Parameters in Discrete-Time Abstract Parabolic Systems with Application to the Transdermal Transport of Alcohol
Prohorov Metric-Based Nonparametric Estimation of the Distribution of Random Parameters in Abstract Parabolic Systems with Application to the Transdermal Transport of Alcohol
Deconvolving the Input to Random Abstract Parabolic Systems; A Population Model-Based Approach to Estimating Blood/Breath Alcohol Concentration from Transdermal Alcohol Biosensor Data
