Localisation Inverse Problem of Absorbing Laplacian Transport


We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely soluble. In this paper, we show that the conformal mapping technique is adopted to this type of problem in the two dimensional case.

Share and Cite:

I. Baydoun, "Localisation Inverse Problem of Absorbing Laplacian Transport," Journal of Modern Physics, Vol. 4 No. 5, 2013, pp. 572-578. doi: 10.4236/jmp.2013.45080.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Lee and G. Uhlmann, Communications on Pure and Applied Mathematics, Vol. 42, 1989, pp. 1097-1112. doi:10.1002/cpa.3160420804
[2] D. C. Barber and B. H. Brown, Journal of Physics E: Scientific Instruments, Vol. 17, 1984, pp. 723-733. doi:10.1088/0022-3735/17/9/002
[3] M. E. Taylor, “Pseudodifferential Operators,” Princeton University Press, Princeton, 1996.
[4] A. Greenleaf and G. Uhlmann, Duke Mathematical Journal, Vol. 108, 2001, pp. 599-617. doi:10.1215/S0012-7094-01-10837-5
[5] B. Sapoval, Physical Review Letters, Vol. 73, 1994, pp. 3314-3316. doi:10.1103/PhysRevLett.73.3314
[6] D. S. Grebenkov, M. Filoche and B. Sapoval, Physical Review E, Vol. 73, 2006, Article ID: 021103. doi:10.1103/PhysRevE.73.021103
[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 City, 2001.
[9] D. Tataru, Communications in Partial Differential Equations, Vol. 20, 1995, pp. 855-884.
[10] I. Baydoun, “Opérateurs de Dirichlet-Neumann et Leurs Applications: Transport Laplacien, Problème Inverse et Opérateur de Dirichlet-Neumann,” éditions Universitaires Européennes, 2012.
[11] I. Baydoun and V. A. Zagrebnov, Theoretical and Mathematical Physics, Vol. 168, 2011, pp. 1180-1191. doi:10.1007/s11232-011-0097-8

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.