Localisation Inverse Problem and Dirichlet-to-Neumann Operator for Absorbing Laplacian Transport

Ibrahim Baydoun

école centrale Paris, Laboratoire de MSS-MAT, F-92295 Grande voie des Vignes, Chatenay-Malabry cedex, France.

DOI: 10.4236/jmp.2013.46106                

Abstract

We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet-to-Neumann operator . In this paper, we define explicitly operator , and we show that Green-Ostrogradski theorem is adopted to this type of problem in three dimensional case.

Keywords

Absorbing Laplacian Transport; Dirichlet-to-Neumann Operators; Inverse Problem

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. Lee and G. Uhlmann, Communications on Pure and Applied Mathematics, Vol. 42, 1989, pp. 1097-1112. doi:10.1002/cpa.3160420804
[2]	B. Sapoval, Physical Review Letters, Vol. 73, 1994, pp. 3314-3316. doi:10.1103/PhysRevLett.73.3314
[3]	D. S. Grebenkov, M. Filoche and B. Sapoval, Physical Revie E, Vol. 73, 2006, Article ID: 021103. doi:10.1103/PhysRevE.73.021103
[4]	O. Kellog, “Foundation of Potential Theory,” Dover, New York, 1954.
[5]	I. Baydoun and V. A. Zagrebnov, Theoretical and Mathematical Physics, Vol. 168, 2011, pp. 1180-1191. doi:10.1007/s11232-011-0097-8
[6]	I. Baydoun, Journal of Modern Physics, 2013, in Press, Article ID: 7501125.
[7]	M. E. Taylor, “Partial Differential Equations II: Qualitative Studies of Linear Equations,” Springer-Verlag, Berlin, 1996. doi:10.1007/978-1-4757-4187-2
[8]	J. K. Hunter and B. Nachtergaele, “Applied Analysis,” World Scientific, Singapore, 2001.
[9]	D. Tataru, Communications in Partial Differential Equations, Vol. 20, 1995, pp. 855-884. doi:10.1080/03605309508821117
[10]	I. Baydoun, Operateurs de Dirichlet-Neumann et leurs applications. Editions universitaires europeennes. 978-3-417-9078-1, 2012.