Stability estimates for solutions of boundary control problems for Maxwell’s equations with mixed boundary conditions. (English. Russian summary) Zbl 1457.35076
Dokl. Math. 86, No. 3, 733-737 (2012); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 447, No. 1, 7-12 (2012).
MSC:
| 35Q61 | Maxwell equations |
| 35M12 | Boundary value problems for PDEs of mixed type |
| 35B35 | Stability in context of PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 78A30 | Electro- and magnetostatics |
| 93B30 | System identification |
References:
| [1] | T. S. Angell and A. Kirsch, SIAM. J. Appl. Math. 52, 1597–1610 (1992). · Zbl 0786.35127 · doi:10.1137/0152092 |
| [2] | D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1998). · Zbl 0893.35138 |
| [3] | F. Cakoni and D. Colton, SIAM J. Appl. Math. 64, 709–723 (2004). · Zbl 1059.35163 · doi:10.1137/S0036139903424254 |
| [4] | F. Cakoni, D. Colton, and P. Monk, Proc. R. Soc. Edinburg 134, 661–682 (2004). · Zbl 1071.78021 · doi:10.1017/S0308210500003413 |
| [5] | R. V. Brizitskii and A. S. Savenkova, Comput. Math. Math. Phys. 50, 984–992 (2010). · Zbl 1224.78007 · doi:10.1134/S0965542510060060 |
| [6] | G. V. Alekseev and R. V. Brizitskii, J. Appl. Ind. Math. 5, 478–490 (2011). · doi:10.1134/S1990478911040028 |
| [7] | V. G. Romanov and S. I. Kabanikhin, Inverse Problems for Maxwell’s Equations (VSP, Utrecht, 1994). · Zbl 0853.35001 |
| [8] | V. G. Romanov, Dokl. Math. 66, 200–205 (2002). |
| [9] | A. E. Dubinov and L. A. Mytareva, Usp. Fiz. Nauk 180, 476–501 (2010). · doi:10.3367/UFNr.0180.201005b.0475 |
| [10] | Yu. I. Bobrovnitskii, Phys.-Dokl. 57, 18–22 (2012). · doi:10.1134/S1028335812010028 |
| [11] | P. Fernandes and G. Gilardi, Math. Mod. Meth. Appl. Sci. 7, 957–991 (1997). · Zbl 0910.35123 · doi:10.1142/S0218202597000487 |
| [12] | G. V. Alekseev, Optimization in Stationary Problems of Heat and Mass Transfer and Magnetohydrodynamics (Nauchnyi Mir, Moscow, 2010) [in Russian]. |
| [13] | M. Costabel, Math. Meth. Appl. Sci. 12, 365–368 (1990). · Zbl 0699.35028 · doi:10.1002/mma.1670120406 |
| [14] | A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems (Nauka, Moscow, 1974; Elsevier, Amsterdam, 1978). |
| [15] | G. V. Alekseev and R. V. Brizitskii, Differ. Equations 46, 70–82 (2010). · Zbl 1193.35247 · doi:10.1134/S0012266110010088 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
