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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 7
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Articles

Stability estimates for some parameters of a reaction-diffusion equation coupled with an ODE

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Pages 1138-1145 | Received 08 Sep 2015, Accepted 12 Apr 2016, Published online: 09 May 2016

References

  • Sundnes J, Lines GT, Cai X, et al. Computing the electrical activity in the heart. Vol. 1, Monographs in computational science and engineering. Berlin: Springer-Verlag; 2006.
  • Bukhgeim A, Klibanov M. Global uniqueness of a class of inverse problems. Sov. Math. Dokl. 1982;24:244–247.
  • Klibanov MV. Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. J. Inverse Ill-Posed Probl. 2013;21:477–560.
  • Yamamoto M. Carleman estimates for parabolic equations and applications. Inverse Probl. 2009;25.
  • Guerrero S, Imanuvilov OYu. Remarks on non controllability of the heat equation with memory. ESAIM Control Optim. Calc. Var. 2013;19:288–300.
  • Chaves-Silva FW, Rosier L, Zuazua E. Null controllability of a system of viscoelasticity with a moving control. J. Math. Pures Appl. 2014;1:198–222.
  • Cristofol M, Roques L. Stable estimation of two coefficients in a nonlinear Fisher-KPP equation. Inverse Probl. 2013;29:095007, 18 pp.
  • Cristofol M, Gaitan P, Ramoul H, et al. Identification of two coefficients with data of one component for a nonlinear parabolic system. Appl. Anal. 2012;91:2073–2081.
  • Boulakia M, Grandmont C, Osses A. Some inverse stability results for the bistable reaction--diffusion equation using carleman inequalities. C.R. Math. Acad. Sci. Paris, Ser. I. 2009;347:619–622.
  • Fursikov AV, Imanuvilov OYu. Controllability of evolution equations. Vol. 34, Lecture notes series. Seoul: Seoul National University Research Institute of Mathematics Global Analysis Research Center; 1996.
  • Fernández-Cara E, González-Burgos M, Guerrero S, et al. Null controllability of the heat equation with boundary Fourier conditions: the linear case. ESAIM Control Optim. Calc. Var. 2006;12:442–465.

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