Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Convergence to stationary states in the Maxwell-Bloch system from nonlinear optics


Author: Frank Jochmann
Journal: Quart. Appl. Math. 60 (2002), 317-339
MSC: Primary 78A60; Secondary 35Q60, 78A25
DOI: https://doi.org/10.1090/qam/1900496
MathSciNet review: MR1900496
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  • [1] J. M. Ball, Strongly continuous semigroups, weak solutions and the variation of constants formula, Proc. Amer. Math. Soc. 63, 370-373 (1977) MR 0442748
  • [2] R. Boyd, Nonlinear Optics, Academic Press, New York, 1992 MR 2475397
  • [3] G. Carbou and P. Fabrie, Time average in micromagnetism, J. Differential Equations 147, 383-409 (1998) MR 1633953
  • [4] C. M. Dafermos, Asymptotic behavior of solutions of evolution equations, Nonlinear Evolution Equations, Academic Press, New York, 1978, pp. 103-123 MR 513814
  • [5] P. Donnat and J. Rauch, Global solvability of the Maxwell-Bloch equations from nonlinear optics, Arch. Rational Mech. Anal. 136, 291-303 (1996) MR 1423010
  • [6] A. Haraux, Stabilization of trajectories for some weakly damped hyperbolic equations, J. Differential Equations 59, 145-154 (1985) MR 804885
  • [7] F. Jochmann, Convergence to stationary states of solutions of the transient drift diffusion equations for semiconductor devices with prescribed currents, Asymptotic Anal. 18, 67-109 (1998) MR 1657481
  • [8] F. Jochmann, Asymptotic behaviour of solutions to a class of semilinear hyperbolic systems in arbitrary domains, J. Differential Equations 60, 439-466 (2000) MR 1736995
  • [9] J. L. Joly, G. Metivier and J. Rauch, Global solvability of the anharmonic oscillator model from nonlinear optics, SIAM J. Math. Anal. 27, 905-913 (1996) MR 1393415
  • [10] L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, New York, 1960
  • [11] R. Pantell and H. Puthoff, Fundamentals of quantum electronics, John Wiley and Sons, New York, 1969
  • [12] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983 MR 710486
  • [13] M. Slemrod, Weak asymptotic decay via a relaxed invariance principle for a wave equation with nonlinear nonmonotone damping, Proc. Roy. Soc. Edinburgh 113A, 87-97 (1989) MR 1025456

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DOI: https://doi.org/10.1090/qam/1900496
Article copyright: © Copyright 2002 American Mathematical Society

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