P. Martinez

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math.OC2018

Null controllability of parabolic equations with interior degeneracy and one-sided control

Piermarco Cannarsa, Roberto Ferretti, Patrick Martinez

For $α \in (0, 2)$ we study the null controllability of the parabolic operator $P u = u_{t} - (∣ x ∣^{α} u_{x})_{x} (1 < x < 1),$ which degenerates at the interior point $x = 0$ , for…

math.OC2018

The cost of controlling strongly degenerate parabolic equations

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble

We consider the typical one-dimensional strongly degenerate parabolic operator $P u = u_{t} - (x^{α} u_{x})_{x}$ with $0 < x < ℓ$ and $α \in (0, 2)$ , controlled either by a boundary control actin…

math.OC2017

Precise estimates for biorthogonal families under asymptotic gap conditions

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble

A classical and useful way to study controllability problems is the moment method developed by Fattorini-Russell, based on the construction of suitable biorthogonal families. Sever…