Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Decay of the electromagnetic field in a Maxwell Bloch system


Author: Frank Jochmann
Journal: Quart. Appl. Math. 65 (2007), 99-112
MSC (2000): Primary 35Q60; Secondary 35L40, 78A35
DOI: https://doi.org/10.1090/S0033-569X-07-01040-5
Published electronically: January 2, 2007
MathSciNet review: 2313150
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the initial-boundary value problem for the Maxwell-Bloch system which describes the propagation of electromagnetic waves in a polarized quantum-mechanical medium with two energy levels. The main goal is the investigation of the large-time asymptotic behavior of the solutions if there are no relaxation terms in the equations governing the polarization field and the density.


References [Enhancements On Off] (What's this?)

  • 1. A. Adams, Sobolev Spaces, Academic Press, 1980.
  • 2. R. Boyd, Nonlinear Optics, Academic Press, (1992).
  • 3. P. Donnat, J. Rauch, Global solvability of the Maxwell-Bloch equations from nonlinear optics. Arch. Rat. Mech. Anal. 136 (1996), 291-303. MR 1423010 (97k:78029)
  • 4. E. Dumas, Global existence for Maxwell-Bloch systems, J. Diff. Equations, 219 (2005), 484-509. MR 2183269 (2006h:35258)
  • 5. F. Jochmann, A compactness result for vector fields with divergence and curl in $ L^q(\Omega)$ involving mixed boundary conditions, Appl. Anal. 66 (1997), 189-203. MR 1612136
  • 6. F. Jochmann, Asymptotic behaviour of solutions to a class of semilinear hyperbolic systems in arbitrary domains, J. Diff. Equations 160 (2000), 439-466. MR 1736995 (2001d:35131)
  • 7. F. Jochmann , Long time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics, SIAM J. Math. Anal. 32 (2000), 887-915. MR 1814743 (2002b:78016)
  • 8. F. Jochmann, Convergence to stationary states in the Maxwell-Bloch system from nonlinear optics, Quart. Appl. Math. 60 (2002), 317-339. MR 1900496 (2003e:78025)
  • 9. F. Jochmann, Decay of the polarization field in a Maxwell Bloch system, Discr. Cont. Dyn. Syst. 9 (2003), 663-676. MR 1974532 (2005a:35267)
  • 10. Joly, J. L., Metivier, G., Rauch, J., Global solvability of the anharmonic oscillator model from nonlinear optics, SIAM J. Math. Anal. 27 (1996), 905-913. MR 1393415 (97f:78023)
  • 11. R. Pantell, H. Puthoff, Fundamental of quantum electronics, Wiley (1969).
  • 12. A. Pazy, (1983): Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, New York. MR 0710486 (85g:47061)
  • 13. J. Rauch, M. Taylor, Penetrations into shadow regions and unique continuation properties in hyperbolic mixed problems, Ind Univ. Math. J. 22 (1972/73), 277-285. MR 0303098 (46:2240)
  • 14. C. Weber, A local compactness theorem for Maxwell's equations, Math. Methods Appl. Sci. 2 (1980), 12-25. MR 0561375 (81f:78005)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35Q60, 35L40, 78A35

Retrieve articles in all journals with MSC (2000): 35Q60, 35L40, 78A35


Additional Information

Frank Jochmann
Affiliation: Technische Universität Berlin, Fakultät II - Mathematik und Naturwissenschaften, Institut für Mathematik, Strasse des 17. Juni 136, 10623 Berlin, Germany
Email: jochmann@math.tu-berlin.de

DOI: https://doi.org/10.1090/S0033-569X-07-01040-5
Received by editor(s): March 27, 2006
Published electronically: January 2, 2007
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society