On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension

Pierre Lissy

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arXiv · 1309.1943

On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension

Pierre Lissy

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Abstract

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in "New blow-up rates for fast controls of Schrödinger and heat equations`", we are able to give precise upper bounds on the time-dependance of the cost of fast controls when the time of control T tends to 0. We also give a lower bound of the cost of fast controls for the same class of equations, which proves the optimality of the power of T involved in the cost of the control. These general results are then applied to treat notably the case of linear KdV equations and fractional heat or Schrödinger equations.

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Pierre Lissy. 2013-09-08. On the cost of fast controls for some families of dispersive or parabolic equations in one space dimension. https://arxiv.org/abs/1309.1943

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