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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 15
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Original Articles

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

Bianca-Elena AramăFaculty of Mathematics, “Alexandru Ioan Cuza” University of Iaşi, Iaşi, Romania.Correspondence[email protected]
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Pages 2619-2634 | Received 27 Mar 2015, Accepted 11 Sep 2016, Published online: 27 Sep 2016

References

  • Moores JD. On the Ginzburg-Landau laser mode-locking model with fifth-order saturable absorber term. Opt. Commun. 1993;96:65–70.
  • Akhmediev NN, Ankiewicz A. Solitons: Nonlinear pulses and beams. London: Chapman & Hall; 1997.
  • Mandel P, Tlidi M. Transverse dynamics in cavity nonlinear optics. J. Opt. B.: Quantum Semiclassical Opt. 2004;6:R60–R75.
  • Chomaz JM. Global instabilities in spatially developing flows: non-normality and nonlinearity. Annual review of fluid mechanics. Vol. 37. Palo Alto (CA): Annual reviews; 2005. p. 357–392.
  • Chomaz JM, Huerre P, Redekopp LG. Bifurcations to local and global modes in spatially developing flows. Phys. Rev. Lett. 1998;60:25–28.
  • Cossu C. Chomaz JM, Global measures of local convective instabilities. Phys. Rev. Lett. 1997;78:4387–4390.
  • Rosier L, Zhang BY. Null controllability of the complex Ginzburg--Landau equation. Ann. Inst. Henri Poincar\’{e}. 2009;AN 26:649–673.
  • Fursikov A, Imanuvilov OY. Controllability of evolution equations. Vol. 34, Lecture notes series. Korea: Seoul National University; 1996.
  • Fernández-Cara E, Zuazua E. The cost of approximate controllability for heat equations: the linear case. Adv. Differ. Equ. 2000;4--6:465–514.
  • Albano P, Tătaru D. Unique continuation for second-order parabolic operators at the initial time. Proc. Am. Math. Soc. 2004;132:1077–1085.
  • Lefter CG, Lorenzi A. Approximate controllability for an integro-differential control problem. Appl. Anal. 2008;91:1529–1549.
  • Lions JL. Remarks on approximate controllability. J. Anal. Math. 1992;59:103–116.
  • Saut JC, Scheurer B. Unique continuation for some evolution equations. J. Differ. Equ. 1987;66:118–139.
  • Fabre C, Puel JP, Zuazua E. Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh. 1995:31–61.
  • Krantz SG. A handbook of real variables. With applications to differential equations and Fourier analysis. Boston (MA): Birkhäuser Boston Inc.; 2004.

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