Inverse problem for the identification of a memory kernel from Maxwell’s system integro-differential equations for a homogeneous anisotropic media
https://doi.org/10.17586/2220-8054-2015-6-2-268-273
Abstract
We consider the problem of reconstructing the time-dependent history of electromagnetic fields from Maxwell’s system of equations for an homogeneous anisotropic medium. As additional information, the Fourier image of electric and magnetic field intensity vectors for values ν = 0 of transformation parameter are given. It is shown that if the given functions satisfy some conditions of agreement and smoothness, the solution of the posed problem is uniquely defined in a class of continuously differentiable functions.
References
1. Landau L. D. and Lifshits E. M. Continuum Electrodynamics. Nauka, Moscow, 1959. (in Russian)
2. Durdiev D. K. An inverse problem for a three-dimensional wave equation in the medium with memory. Math. Anal. and Disc. Math., Novosibirsk, NGU, P. 19–26 (1989). (in Russian)
3. Durdiev D. K. To the question of correctness of one inverse problem for hyperbolic integro-differential equation. Sib. Math. Journ., 33 (3), P. 69–77 (1992). (in Russian)
4. Lorensi A. An identification problem related to a nonlinear hyperbolic integro-differential equation. Nonlinear Analysis: Theory, Methods and Applications, 22, P. 297–321 (1994).
5. Janno J. and Von Welfersdorf L. Inverse problems for identification of memory kernels in viscoelasticity. Math. Methods in Appl. Sciences, 20 (4), P. 291–314 (1997).
6. Durdiev D. K. Global solvability of an inverse problem for an integro-differential equation of electrodynamics. Differential Equations, (44) (7), P. 893–899 (2008).
7. Jaan J. and Von Wolfersdorf L. An inverse problem for identification of a time- and space-dependent memory kernel in viscoelasticity. Inverse Problems, 17, P. 13–24 (2001).
8. Colombo F. and Guidetti D. A global in time existence and uniqueness result for a semilinear integrodifferential parabolic inverse problem in Sobolev spaces. Math. Methods in Appl. Sciences, 17, P. 1–29 (2007).
9. Colombo F. and Guidetti D. Some results on the Identification of memory kernels. Oper. Theory: Adv. Appl., 216, P. 121–138 (2011).
10. Favaron A. Identification of Memory Kernels Depending on Time and on an Angular Variable. Zeitschrift fur Analysis und ihre Anwendungen, 24, (4), P. 735–762 (2005).
11. Romanov V. G. Inverse problems of mathematical physics. Nauka, Moscow, 1984. (in Russian)
Review
For citations:
Durdiev D.K. Inverse problem for the identification of a memory kernel from Maxwell’s system integro-differential equations for a homogeneous anisotropic media. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(2):268-273. https://doi.org/10.17586/2220-8054-2015-6-2-268-273
Views:
6
Email this article 