Far Eastern Mathematical Journal

To content of the issue


Boundary Value Problem for the Transfer Equation of Amplitude Modulated Radiation


I. V. Prokhorov, V. M. Moon

2009, issue 1-2, P. 150–160


Abstract
In the paper а class of solutions of the non-stationary radiative transfer equation with the harmonic time-dependence have been considered. In this class solubility of the boundary-value problem with generalized matching conditions on the interface are proved and estimations for the solutions are obtained.

Keywords:
radiation transport theory, boundary value problems

Download the article (PDF-file)

References

[1] A. Isimaru, Rasprostranenie i rasseyanie voln v sluchajno-neodnorodnyx sredax, Mir, M., 1981.
[2] K. Kejz, P. Cvajfel', Linejnaya teoriya perenosa, Mir, M., 1972.
[3] V. V. Tuchin, “Issledovanie biotkanej metodami svetorasseyaniya”, Uspexi fizicheskix nauk, 167:5 (1997), 517–539.
[4] S. R. Arridge, “Optical tomography in medical imaging”, Inverse Problems, 15:2 (1999), R41–R93.
[5] K. Ren, G. S. Abdoulaev, G. Bal, A. H. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain”, Optics Letters, 29:6 (2004), 578–580.
[6] K. Ren, G. Bal, A. Hielscher, “Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer”, SIAM Journal on Scientific Computing, 28:4 (2006), 1463–1489.
[7] V. S. Vladimirov, “Matematicheskie zadachi odnoskorostnoj teorii perenosa chastic”, Tr. MIAN SSSR, 61, 1961, 3–158.
[8] T. A. Germogenova, Lokal'nye svojstva reshenij uravneniya perenosa, Nauka, M., 1986.
[9] I. V. Proxorov, “Kraevaya zadacha teorii perenosa izlucheniya v neodnorodnoj srede s usloviyami otrazheniya na granice”, Differencial'nye uravneniya, 36:6 (2000), 848–851.
[10] I. V. Proxorov, “O razreshimosti kraevoj zadachi dlya uravneniya perenosa izlucheniya s obobshhennymi usloviyami sopryazheniya na granice razdela sred”, Izvestiya RAN. Seriya matematicheskaya, 67:6 (2003), 169–192.
[11] I. V. Prokhorov, I. P. Yarovenko, and T. V. Krasnikova, “An extremum problem for the radiation transfer equation”, Journal of Inverse and Ill-Posed Problems, 13:4 (2005), 365–382.
[12] I. V. Proxorov, “Opredelenie poverxnosti razdela sred po dannym tomograficheskogo prosvechivaniya”, Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki, 42:10 (2002), 1542–1555.
[13] I. V. Proxorov, I. P. Yarovenko, “Issledovanie zadach opticheskoj tomografii metodami teorii perenosa izlucheniya”, Optika i spektroskopiya, 101:5 (2006), 817–824.
[14] I. V. Prokhorov, I. P. Yarovenko, V. G. Nazarov, “Optical tomography problems at layered media”, Inverse Problems, 24:2 (2008), 025019.
[15] Anikonov D.S., A. E. Kovtanyuk and I. V. Prokhorov, Transport Equation and Tomography, VSP, Utrecht – Boston, 2002.
[16] M. Born, E'. Vol'f, Osnovy optiki, Nauka, M., 1973.

To content of the issue