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On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$
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Analysis and simulation for an isotropic phase-field model describing grain growth
Identification problems related to cylindrical dielectrics **in presence of polarization**
| 1. | Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano |
For this problem, under some additional measurement, we prove an existence and uniqueness result.
References:
| [1] |
H. T. Banks and G. A. Pinter, Maxwell-systems with nonlinear polarization, Nonlinear Anal. Real World Appl., 4 (2003), 483-501.
doi: 10.1016/S1468-1218(02)00074-3. |
| [2] |
H. T. Banks and N. L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters, Appl. Math. Lett., 18 (2005), 423-430.
doi: 10.1016/j.aml.2004.02.008. |
| [3] |
M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Math. Methods Appl. Sci., 12 (1990), 365-368.
doi: 10.1002/mma.1670120406. |
| [4] |
V. Girault and P. A. Raviart, Finite Element Approximation Of The Navier-Stokes Equations, Lecture notes in Mathematics vol. 749, Springer Verlag, Berlin 1979. |
| [5] |
F. Jochmann, Energy decay of solutions to Maxwell's equations with conductivity and polarization, J. Differential Equations, 203 (2004), 232-254.
doi: 10.1016/j.jde.2004.05.005. |
| [6] |
F. Jochmann, Exponential decay of solutions of Maxwell's equations coupled with a first-order ordinary differential equation for the polarization, J. Math. Anal. Appl., 288 (2003), 411-423.
doi: 10.1016/j.jmaa.2003.08.052. |
| [7] |
A. Lorenzi and V. I. Priimenko, Identification problems related to electro-magneto-elastic interactions, J. Inverse Ill Posed Probl., 4 (1996), 115-143.
doi: 10.1515/jiip.1996.4.2.115. |
| [8] |
A. L. Nazarov and V. G. Romanov, A uniqueness theorem in the inverse problem for the integrodifferential electrodynamics equations, Sibirskii Zhurnal Industrial'noi Mathematiki, 15 (2012), 77-86 (in Russian); English translation in Journal of Applied and Industrial Mathematics, 6 (2012), 460-468.
doi: 10.1134/S1990478912040072. |
| [9] |
V. G. Romanov, Problem of kernel recovering for the viscoelasticity equation, Doklady Akademii Nauk, 446 (2012), 18-20; English transl. in Doklady Mathematics, 86 (2012), 608-610.
doi: 10.1134/S1064562412050067. |
| [10] |
D. Sheen, A generalized Green's theorem, Appl. Math. Lett., 5 (1992), 95-98.
doi: 10.1016/0893-9659(92)90096-R. |
show all references
References:
| [1] |
H. T. Banks and G. A. Pinter, Maxwell-systems with nonlinear polarization, Nonlinear Anal. Real World Appl., 4 (2003), 483-501.
doi: 10.1016/S1468-1218(02)00074-3. |
| [2] |
H. T. Banks and N. L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters, Appl. Math. Lett., 18 (2005), 423-430.
doi: 10.1016/j.aml.2004.02.008. |
| [3] |
M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains, Math. Methods Appl. Sci., 12 (1990), 365-368.
doi: 10.1002/mma.1670120406. |
| [4] |
V. Girault and P. A. Raviart, Finite Element Approximation Of The Navier-Stokes Equations, Lecture notes in Mathematics vol. 749, Springer Verlag, Berlin 1979. |
| [5] |
F. Jochmann, Energy decay of solutions to Maxwell's equations with conductivity and polarization, J. Differential Equations, 203 (2004), 232-254.
doi: 10.1016/j.jde.2004.05.005. |
| [6] |
F. Jochmann, Exponential decay of solutions of Maxwell's equations coupled with a first-order ordinary differential equation for the polarization, J. Math. Anal. Appl., 288 (2003), 411-423.
doi: 10.1016/j.jmaa.2003.08.052. |
| [7] |
A. Lorenzi and V. I. Priimenko, Identification problems related to electro-magneto-elastic interactions, J. Inverse Ill Posed Probl., 4 (1996), 115-143.
doi: 10.1515/jiip.1996.4.2.115. |
| [8] |
A. L. Nazarov and V. G. Romanov, A uniqueness theorem in the inverse problem for the integrodifferential electrodynamics equations, Sibirskii Zhurnal Industrial'noi Mathematiki, 15 (2012), 77-86 (in Russian); English translation in Journal of Applied and Industrial Mathematics, 6 (2012), 460-468.
doi: 10.1134/S1990478912040072. |
| [9] |
V. G. Romanov, Problem of kernel recovering for the viscoelasticity equation, Doklady Akademii Nauk, 446 (2012), 18-20; English transl. in Doklady Mathematics, 86 (2012), 608-610.
doi: 10.1134/S1064562412050067. |
| [10] |
D. Sheen, A generalized Green's theorem, Appl. Math. Lett., 5 (1992), 95-98.
doi: 10.1016/0893-9659(92)90096-R. |
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