Quetelet: An approach of Probability Theory and Statistics.
Let P be a stochastic matrix. We give a necessary and sufficient condition for the existence of the lim p from which follows the classical regularity conditions. Another regularity condition based in the Banach point fix theorem is also given.
In this paper, we consider a one-dimensional system governed by two partial differential equations. Such a system models phenomena in engineering, such as vibrations in beams or deformation of elastic bodies with porosity. By using the HUM method, we prove that the system is boundary exactly controllable in the usual energy space. We will also determine the minimum time allowed by the method for the controllability to occur.
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