References
- Kernévez JP . The sentinel method and its application to environmental pollution problems. Vol. 7. New York: CRC Press; 1997.
- Okubo A , Levin SA . Diffusion and ecological problems: modern perspectives. Vol. 14. New York: Springer Science & Business Media; 2013.
- Hamdi A . A non-iterative method for identifying multiple unknown time-dependent sources compactly supported occurring in a 2d parabolic equation. Inverse Probl Sci Eng. 2017;26(5):744–772.
- Andrle M , Belgacem FB , El Badia A . Identification of moving pointwise sources in an advection-dispersion-reaction equation. Inverse Probl. 2011;27(2):025007.
- Andrle M , El Badia A . Identification of multiple moving pollution sources in surface waters or atmospheric media with boundary observations. Inverse Probl. 2012;28(7):075009.
- Yamamoto M . Conditional stability in determination of densities of heat sources in a bounded domain. Int Ser Numer Math. 1994;18:359–359.
- El Badia A , Ha-Duong T . On an inverse source problem for the heat equation. application to a pollution detection problem. J Inverse Ill-posed Probl. 2002;10(6):585–599.
- Andrle M , El Badia A . On an inverse source problem for the heat equation. application to a pollution detection problem, ii. Inverse Probl Sci Eng. 2015;23(3):389–412.
- Auffray N , Bonnet M , Pagano S . Identification de sources de chaleur dans le contexte de la thermographie infrarouge. In: 10e colloque national en calcul des structures; 2011. p. 8-p.
- Hettlich F , Rundell W . Identification of a discontinuous source in the heat equation. Inverse Probl. 2001;17(5):1465–1482.
- Harbrecht H , Tausch J . An efficient numerical method for a shape-identification problem arising from the heat equation. Inverse Probl. 2011;27(6):065013.
- Canelas A , Laurain A , Novotny AA . A new reconstruction method for the inverse source problem from partial boundary measurements. Inverse Probl. 2015;31(7):075009.
- Garreau S , Guillaume P , Masmoudi M . The topological asymptotic for pde systems: the elasticity case. SIAM J Control Optim. 2001;39(6):1756–1778.
- Abda AB , Hassine M , Jaoua M , et al . Topological sensitivity analysis for the location of small cavities in stokes flow. SIAM J Control Optim. 2009;48(5):2871–2900.
- Larnier S , Masmoudi M . The extended adjoint method. ESAIM: Math Modell Numer Anal. 2013;47(1):83–108.
- Samet B , Amstutz S , Masmoudi M . The topological asymptotic for the helmholtz equation. SIAM J Control Optim. 2003;42(5):1523–1544.
- Hassine M , Hrizi M . Topological sensitivity analysis for reconstruction of the inverse source problem from boundary measurement. World Acad Sci Eng Technol Int J Math, Comput Phys Elect Comput Eng. 11(1):26–32.
- Isakov V . Inverse source problems. Vol. 34. Providence, Rhode Islande: American Mathematical Society; 1990.
- Cannon J , Perez-Esteva S . Uniqueness and stability of 3d heat sources. Inverse Probl. 1991;7(1):57–62.
- Choulli M . Une introduction aux problčmes inverses elliptiques et paraboliques. Vol. 65. Berlin: Springer Science & Business Media; 2009.
- Schumacher A . Topologieoptimierung von bauteilstrukturen unter verwendung von lochpositionierungskriterien [PhD thesis]. Forschungszentrum für Multidisziplinäre Analysen und Angewandte Strukturoptimierung. Institut für Mechanik und Regelungstechnik; 1996.
- Sokolowski J , Zochowski A . On the topological derivative in shape optimization. SIAM J Control Optim. 1999;37(4):1251–1272.
- Masmoudi M . The topological asymptotic, computational methods for control applications. In: kawarada H , périaux J , editors. International series. Gakuto; 2002.
- Amstutz S . Sensitivity analysis with respect to a local perturbation of the material property. Asym Anal. 2006;49(1, 2):87–108.
- Amstutz S , Takahashi T , Vexler B . Topological sensitivity analysis for time-dependent problems. ESAIM: Control Optim Cal Var. 2008;14(3):427–455.
- Amstutz S , Horchani I , Masmoudi M . Crack detection by the topological gradient method. Control Cybern. 2005;34(1):81–101.
- Novotny AA , Sokołowski J . Topological derivatives in shape optimization. Berlin, Heidelberg: Springer Science & Business Media; 2012.
- Brezis H . Functional analysis, sobolev spaces and partial differential equations. New York: Springer Science & Business Media; 2010.
- Ferchichi J , Hassine M , Khenous H . Detection of point-forces location using topological algorithm in stokes flows. Appl Math Comput. 2013;219(12):7056–7074.
- Hrizi M , Hassine M . One-iteration reconstruction algorithm for geometric inverse source problem. J Elliptic Parabolic Equ. 4(1):177–205.