The cost of approximate controllability and a unique continuation result at initial time for the Ginzburg-Landau equation

Abstract

We reconsider the Carleman inequalities for the linearized Ginzburg–Landau equation and obtain explicit estimates with respect to T, where is the time interval we consider. We apply these Carleman inequalities to obtain explicit bounds for the cost of approximate controllability and also to prove a unique continuation result at initial time.

Keywords:

• Ginzburg–Landau equation
• Carleman estimates
• approximate controllability
• unique continuation

AMS Subject Classifications:

• Primary: 35Q56
• Secondary: 93B05
• 93B07
• 93B18
• 93C10

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the strategic [grant number POSDRU/159/1.5/S/137750], Project “Doctoral and Postdoctoral programs support for increased competitiveness in Exact Sciences research” cofinanced by the European Social Found within the Sectorial Operational Program Human Resources Development 2007–2013 and by [grant number PN-II-ID-PCE-2012-4-0456].