GLOBAL NON-NEGATIVE APPROXIMATE CONTROLLABILITY OF PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

Judith Vancostenoble (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this work, we consider the linear 1 − d heat equation with some singular potential (typically the so-called inverse square potential). We investigate the global approximate controllability via a multiplicative (or bilinear) control. Provided that the singular potential is not super-critical, we prove that any non-zero and non-negative initial state in L 2 can be steered into any neighborhood of any non-negative target in L 2 using some static bilinear control in L ∞. Besides the corresponding solution remains non-negative at all times.

Domaines: Mathématiques [math]

Judith Vancostenoble. GLOBAL NON-NEGATIVE APPROXIMATE CONTROLLABILITY OF PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS. 2018. ⟨hal-01895349⟩