Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 5
125
Views
1
CrossRef citations to date
0
Altmetric
Articles

Inverse coefficient problem for a magnetohydrodynamics system by Carleman estimates

Pages 1010-1038 | Received 13 Mar 2019, Accepted 10 Jun 2019, Published online: 22 Jun 2019

References

  • Li T, Qin T. Physics and partial differential equations. Vol. 1. Beijing: Higher Education Press; 2013.
  • Fan J, Li J. A logarithmic regularity criterion for the 3D generalized MHD system. Math Methods Appl Sci. 2015. DOI: 10.1002/mma.3480
  • Lin H, Du L. Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions. Nonlinearity. 2013;26:219–239.
  • Li H. Global strong solution to the three dimensional nonhomogeneous incompressible magnetohydrodynamics equations with density-dependent viscosity and resistivity. Math Methods Appl Sci. 2018;41:3062–3092.
  • Havârneanu T, Popa C, Sritharan SS. Exact internal controllability for the magnetohydrodynamic equations in multi-connected domains. Adv Differ Equ. 2006;11:893–929.
  • Havârneanu T, Popa C, Sritharan SS. Exact internal controllability for the two-dimensional magnetohydrodynamic equations. SIAM J Control Optim. 2007;46:1802–1830.
  • Bukhgeim AL, Klibanov MV. Global uniqueness of class of multidimensional inverse problems. Sov Math Dokl. 1981;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.
  • Carleman T. Sur un problème d'unicité pour les systèmes d'équations aux d'rivées partielles à deux variables indépendantes. Ark Mat Astr Fys. 1939;2 B:1–9.
  • Egorov YV. Linear differential equations of principal type. New York (NY): Consultants Bureau; 1986.
  • Hörmander L. The analysis of linear partial differential operators IIV. Berlin: Springer; 1985.
  • Isakov V. Inverse source problems. Providence (RI): American Mathematical Society; 1990.
  • Isakov V. Inverse problems for partial differential equations. Berlin: Springer; 1998.
  • Klibanov MV. A class of inverse problems for nonlinear parabolic equations. Siberian Math J. 1987;27:698–707.
  • Klibanov MV. Inverse problems and Carleman estimates. Inverse Probl. 1992;8:575–596.
  • Tataru D. Carleman estimates and unique continuation for solutions to boundary value problems. J Math Pures Appl. 1996;75:367–408.
  • Taylor M. Pseudodifferential operators. Princeton (NJ): Princeton University Press; 1981.
  • Bellassoued M, Yamamoto M. Carleman estimates and applications to inverse problems for hyperbolic systems. Tokyo: Springer-Japan; 2017.
  • Gaitan P, Ouzzane H. Inverse problem for a free transport equation using Carleman estimates. Appl Anal. 2013. DOI:10.1080/00036811.2013.816686
  • Yamamoto M. Carleman estimates for parabolic equations and applications. Inverse Probl. 2009;25:123013.
  • Bellassoued M, Cristofol M, Soccorsi E. Inverse boundary value problem for the dynamical heterogeneous Maxwell's system. Inverse Probl. 2012;28:095009.
  • Bellassoued M, Imanuvilov OY, Yamamoto M. Inverse problem of determining the density and two Lamé coefficients by boundary data. SIAM J Math Anal. 2008;40:238–265.
  • Choulli M, Imanuvilov OY, Puel J-P, et al. Inverse source problem for linearized Navier–Stokes equations with data in arbitrary sub-domain. Appl Anal. 2013;92:2127–2143.
  • Imanuvilov OY, Puel J-P, Yamamoto M. Carleman estimates for parabolic equations with nonhomogeneous boundary conditions. Chin Ann Math Ser B. 2009;30:333–378.
  • Fursikov AV, Imanuvilov OY. Controllability of evolution equations. Korea: Seoul National University; 1996.
  • Imanuvilov OY, Puel J-P. Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems. Int Math Res Notes. 2003;16:883–913.
  • Bellassoued M, Imanuvilov OY, Yamamoto M. Carleman estimate for the Navier–Stokes equations and an application to a lateral Cauchy problem. Inverse Probl. 2016;32:025001.
  • Adams RA, Fournier JF. Sobolev spaces. Singapore: Academic Press; 2003. (Pure and applied mathematics series; vol. 140).
  • Chae D, Imanuvilov OY, Kim SM. Exact controllability for semilinear parabolic equations with Neumann boundary conditions. J Dyn Control Syst. 1996;2:449–483.
  • Imanuvilov OY. Controllability of parabolic equations. Sbornik Math. 1995;186:879–900.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.