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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 13
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Articles

Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide

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Pages 2210-2228 | Received 22 Dec 2016, Accepted 05 Dec 2018, Published online: 18 Dec 2018

References

  • Murray JD. Mathematical Biology. Vol. 17. New York: Springer; 2002. (Interdisciplinary Applied Mathematics).
  • Bear J. Dynamics of fluids in porous media. New York: Elsevier; 1972.
  • Beck V, Blackwell B, St. Clair CR. Inverse heat conductions, Ill-Posed Problems. New York: Wiley Interscience; 1985.
  • Isakov V. Inverse source problems. Mathematical survey and monograph. Providence (RI): American Mathematical Society; 1990.
  • Cannon JR. Determination of an unknown heat source from overspecified boundary data. SIAM J Numer Anal. 1968;5:275–286. doi: 10.1137/0705024
  • Choulli M, Yamamoto M. Some stability estimates in determining sources and coefficients. J Inverse Ill-Posed Probl. 2004;12(3):233–243. doi: 10.1515/1569394042215856
  • Yamamoto M. Conditional stability in the determination of force terms of heat equations in a rectangle. Math Comput Model. 1993;18:79–88. doi: 10.1016/0895-7177(93)90081-9
  • Yamamoto M. Conditional stability in the determination of densities of heat sources in a bounded domain. In: Desch W, Kappel F, Kunisch K, editor. Estimation and Control of Distributed Parameter Systems. Basel: Birkhäuser Verlag; 1994. p. 359–370.
  • Imanuvilov OY, Yamamoto M. Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Probl. 1998;14:1229–1245. doi: 10.1088/0266-5611/14/5/009
  • Bukhgeim A, Klibanov M. Global uniqueness of a class of multidimensional inverse problem. Sov Math Dokl. 1981;24:244–247.
  • Choulli M, Yamamoto M. Some stability estimates in determining sources and coefficients. J Inverse Ill-Posed Probl. 2006;14(4):355–373. doi: 10.1515/156939406777570996
  • Lions J-L, Magenes E. Problèmes aux limites non homogènes et applications. Paris: Dunod; 1968
  • Choulli M. Une introduction aux problèmes inverses elliptiques et paraboliques. Vol. 65. Berlin, Heidelberg: Springer-Verlag; 2009. (Mathématiques & Applications).
  • Baudouin L, Puel J-P. Uniqueness and stability in an inverse problem for the Schrödinger equation. Inverse Probl. 2002;18:1537–1554. doi: 10.1088/0266-5611/18/6/307
  • Baudouin L, Puel J-P. Corrigendum to Uniqueness and stability in an inverse problem for the Schrödinger equation. Inverse Probl. 2007;23:1327–1328. doi: 10.1088/0266-5611/23/3/C01
  • Kian Y, Phan QS, Soccorsi E. Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains. J Math Anal Appl. 2015;426(1):194–210. doi: 10.1016/j.jmaa.2015.01.028
  • Bellassoued M, Kian Y, Soccorsi E. An inverse stability result for non compactly supported potentials by one arbitrary lateral Neumann observation. J Differ Equ. 2016;260:7535–7562. doi: 10.1016/j.jde.2016.01.033
  • Kian Y, Phan QS, Soccorsi E. Carleman estimate for infinite cylindrical quantum domains and application to inverse problems. Inverse Probl. 2014;30(5):055016. doi: 10.1088/0266-5611/30/5/055016
  • Choulli M, Kian Y, Soccorsi E. Determining the time dependent external potential from the DN map in a periodic quantum waveguide. SIAM J Math Anal. 2015;47(6):4536–4558. doi: 10.1137/140986268
  • Dautray J, Lions J-L. Mathematical analysis and numerical methods for sciences and technology. Berlin Heidelberg: Springer; 1992
  • Fursikov AV, Imanuvilov OY. Controllability of evolution equations. Seoul: Seoul National Univ; 1996. (Lecture Notes Series).
  • Chae D, Yu Imanuvilov O., Kim SM. Exact controllability for semi-linear parabolic equations with Neumann boundary conditions. J Dynam Control Systems. 1996;2(4):449–483. doi: 10.1007/BF02254698
  • Fernández-Cara E. Null controllability of the semilinear heat equation ESAIM. Cont Optim Calc Var. 1997;2:87–103. doi: 10.1051/cocv:1997104

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