Abstract
In this paper, we study the quantitative analyticity and observability inequality for solutions of fractional order parabolic equations with space-time dependent potentials in ℝn. We first obtain a uniformly lower bound of analyticity radius of the spatial variable for the above solutions with respect to the time variable. Next, we prove a globally Hölder-type interpolation inequality on a thick set, which is based on a propagation estimate of smallness for analytic functions. Finally, we establish an observability inequality from a thick set in ℝn, by utilizing a telescoping series method.
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering