• Previous Article
    On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$
  • DCDS-B Home
  • This Issue
  • Next Article
    Analysis and simulation for an isotropic phase-field model describing grain growth
September  2014, 19(7): 2247-2265. doi: 10.3934/dcdsb.2014.19.2247

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

Received  April 2013 Revised  August 2013 Published  August 2014

We consider the problem of recovering a polarization kernel in an axially inhomogeneous cylindrical dielectric, the polarization depending on time and the axial variable, but being constant on each cross section of the cylinder.
    For this problem, under some additional measurement, we prove an existence and uniqueness result.
Citation: Alfredo Lorenzi. Identification problems related to cylindrical dielectrics **in presence of polarization**. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2247-2265. doi: 10.3934/dcdsb.2014.19.2247
References:
[1]

H. T. Banks and G. A. Pinter, Maxwell-systems with nonlinear polarization,, Nonlinear Anal. Real World Appl., 4 (2003), 483.  doi: 10.1016/S1468-1218(02)00074-3.  Google Scholar

[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.  doi: 10.1016/j.aml.2004.02.008.  Google Scholar

[3]

M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains,, Math. Methods Appl. Sci., 12 (1990), 365.  doi: 10.1002/mma.1670120406.  Google Scholar

[4]

V. Girault and P. A. Raviart, Finite Element Approximation Of The Navier-Stokes Equations,, Lecture notes in Mathematics vol. 749, (1979).   Google Scholar

[5]

F. Jochmann, Energy decay of solutions to Maxwell's equations with conductivity and polarization,, J. Differential Equations, 203 (2004), 232.  doi: 10.1016/j.jde.2004.05.005.  Google Scholar

[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.  doi: 10.1016/j.jmaa.2003.08.052.  Google Scholar

[7]

A. Lorenzi and V. I. Priimenko, Identification problems related to electro-magneto-elastic interactions,, J. Inverse Ill Posed Probl., 4 (1996), 115.  doi: 10.1515/jiip.1996.4.2.115.  Google Scholar

[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.  doi: 10.1134/S1990478912040072.  Google Scholar

[9]

V. G. Romanov, Problem of kernel recovering for the viscoelasticity equation,, Doklady Akademii Nauk, 446 (2012), 18.  doi: 10.1134/S1064562412050067.  Google Scholar

[10]

D. Sheen, A generalized Green's theorem,, Appl. Math. Lett., 5 (1992), 95.  doi: 10.1016/0893-9659(92)90096-R.  Google Scholar

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.  doi: 10.1016/S1468-1218(02)00074-3.  Google Scholar

[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.  doi: 10.1016/j.aml.2004.02.008.  Google Scholar

[3]

M. Costabel, A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains,, Math. Methods Appl. Sci., 12 (1990), 365.  doi: 10.1002/mma.1670120406.  Google Scholar

[4]

V. Girault and P. A. Raviart, Finite Element Approximation Of The Navier-Stokes Equations,, Lecture notes in Mathematics vol. 749, (1979).   Google Scholar

[5]

F. Jochmann, Energy decay of solutions to Maxwell's equations with conductivity and polarization,, J. Differential Equations, 203 (2004), 232.  doi: 10.1016/j.jde.2004.05.005.  Google Scholar

[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.  doi: 10.1016/j.jmaa.2003.08.052.  Google Scholar

[7]

A. Lorenzi and V. I. Priimenko, Identification problems related to electro-magneto-elastic interactions,, J. Inverse Ill Posed Probl., 4 (1996), 115.  doi: 10.1515/jiip.1996.4.2.115.  Google Scholar

[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.  doi: 10.1134/S1990478912040072.  Google Scholar

[9]

V. G. Romanov, Problem of kernel recovering for the viscoelasticity equation,, Doklady Akademii Nauk, 446 (2012), 18.  doi: 10.1134/S1064562412050067.  Google Scholar

[10]

D. Sheen, A generalized Green's theorem,, Appl. Math. Lett., 5 (1992), 95.  doi: 10.1016/0893-9659(92)90096-R.  Google Scholar

[1]

Paulo Cesar Carrião, Patrícia L. Cunha, Olímpio Hiroshi Miyagaki. Existence results for the Klein-Gordon-Maxwell equations in higher dimensions with critical exponents. Communications on Pure & Applied Analysis, 2011, 10 (2) : 709-718. doi: 10.3934/cpaa.2011.10.709

[2]

Frank Jochmann. Decay of the polarization field in a Maxwell Bloch system. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 663-676. doi: 10.3934/dcds.2003.9.663

[3]

G. Kamberov. Prescribing mean curvature: existence and uniqueness problems. Electronic Research Announcements, 1998, 4: 4-11.

[4]

Angelo Favini. A general approach to identification problems and applications to partial differential equations. Conference Publications, 2015, 2015 (special) : 428-435. doi: 10.3934/proc.2015.0428

[5]

Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867

[6]

Vicent Caselles. An existence and uniqueness result for flux limited diffusion equations. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1151-1195. doi: 10.3934/dcds.2011.31.1151

[7]

Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure & Applied Analysis, 2006, 5 (1) : 213-240. doi: 10.3934/cpaa.2006.5.213

[8]

Zhifu Xie. General uniqueness results and examples for blow-up solutions of elliptic equations. Conference Publications, 2009, 2009 (Special) : 828-837. doi: 10.3934/proc.2009.2009.828

[9]

Olivier Guibé, Anna Mercaldo. Uniqueness results for noncoercive nonlinear elliptic equations with two lower order terms. Communications on Pure & Applied Analysis, 2008, 7 (1) : 163-192. doi: 10.3934/cpaa.2008.7.163

[10]

Alberto Fiorenza, Anna Mercaldo, Jean Michel Rakotoson. Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 893-906. doi: 10.3934/dcds.2002.8.893

[11]

Jérémi Dardé, Sylvain Ervedoza. Backward uniqueness results for some parabolic equations in an infinite rod. Mathematical Control & Related Fields, 2019, 9 (4) : 673-696. doi: 10.3934/mcrf.2019046

[12]

Yachun Li, Shengguo Zhu. Existence results for compressible radiation hydrodynamic equations with vacuum. Communications on Pure & Applied Analysis, 2015, 14 (3) : 1023-1052. doi: 10.3934/cpaa.2015.14.1023

[13]

Tôn Việt Tạ. Existence results for linear evolution equations of parabolic type. Communications on Pure & Applied Analysis, 2018, 17 (3) : 751-785. doi: 10.3934/cpaa.2018039

[14]

Maria Francesca Betta, Olivier Guibé, Anna Mercaldo. Uniqueness for Neumann problems for nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1023-1048. doi: 10.3934/cpaa.2019050

[15]

Monica Motta, Caterina Sartori. Uniqueness results for boundary value problems arising from finite fuel and other singular and unbounded stochastic control problems. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 513-535. doi: 10.3934/dcds.2008.21.513

[16]

Gabriele Bonanno, Pasquale Candito, Roberto Livrea, Nikolaos S. Papageorgiou. Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1169-1188. doi: 10.3934/cpaa.2017057

[17]

Mingxin Wang. Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 415-421. doi: 10.3934/dcdsb.2018179

[18]

Monica Lazzo. Existence and multiplicity results for a class of nonlinear elliptic problems in $\mathbb(R)^N$. Conference Publications, 2003, 2003 (Special) : 526-535. doi: 10.3934/proc.2003.2003.526

[19]

Antonio Iannizzotto, Nikolaos S. Papageorgiou. Existence and multiplicity results for resonant fractional boundary value problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (3) : 511-532. doi: 10.3934/dcdss.2018028

[20]

Laurence Guillot, Maïtine Bergounioux. Existence and uniqueness results for the gradient vector flow and geodesic active contours mixed model. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1333-1349. doi: 10.3934/cpaa.2009.8.1333

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]