A small domain limit for nonlinear dielectric media
Author:
Frank Jochmann
Journal:
Quart. Appl. Math. 62 (2004), 477-492
MSC:
Primary 35Q60; Secondary 35B25, 78A48
DOI:
https://doi.org/10.1090/qam/2086041
MathSciNet review:
MR2086041
Full-text PDF Free Access
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Additional Information
- Robert W. Boyd, Nonlinear optics, 3rd ed., Elsevier/Academic Press, Amsterdam, 2008. MR 2475397
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- P. Donnat and J. Rauch, Global solvability of the Maxwell-Bloch equations from nonlinear optics, Arch. Rational Mech. Anal. 136 (1996), no. 3, 291–303. MR 1423010, DOI https://doi.org/10.1007/BF02206557
- F. Jochmann, The semistatic limit for Maxwell’s equations in an exterior domain, Comm. Partial Differential Equations 23 (1998), no. 11-12, 2035–2076. MR 1662168, DOI https://doi.org/10.1080/03605309808821410
- Frank Jochmann, Long time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics, SIAM J. Math. Anal. 32 (2000), no. 4, 887–915. MR 1814743, DOI https://doi.org/10.1137/S0036141099360932
- Frank Jochmann, Existence of solutions and a quasi-stationary limit for a hyperbolic system describing ferromagnetism, SIAM J. Math. Anal. 34 (2002), no. 2, 315–340. MR 1951777, DOI https://doi.org/10.1137/S0036141001392293
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- J. L. Joly, G. Métivier, and J. Rauch, Global solutions to Maxwell equations in a ferromagnetic medium, Ann. Henri Poincaré 1 (2000), no. 2, 307–340. MR 1770802, DOI https://doi.org/10.1007/PL00001007
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F. Midwinter, Zernicke, Applied Nonlinear Optics, Wiley, 1972.
- A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486
A. Sauter, Nonlinear Optics, Wiley, 1983.
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A. Visintin, On Landau-Lifschitz equation for ferromagnetism, Japan J. of Appl. Math., 2, No. 1, 69-84.
R. Boyd, Nonlinear Optics, Academic Press, New York, 1992.
J. M. Ball, Strongly continuous semigroups, weak solutions and the variation of constants formula, Proc. Amer. Math. Soc 63 (1977), 370 - 373.
G. Carbou, P. Fabrie, Time average in micromagnetism, J. Diff. Equations. 147 (1998), 383 - 409.
P. Donnat, J. Rauch, Global solvability of the Maxwell Bloch equations from nonlinear optics, Arch. Rat. Mech. Anal. 136 (1996), 291-303.
F. Jochmann, The semistatic limit for Maxwell’s equations in an exterior domain, Comm. Part. Diff. Equations, 23, (1998), 2035-2076.
F. Jochmann, Long time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics, SIAM J. Math. Anal., 32, (2000), 887-915.
F. Jochmann, Existence of solutions and a quasistationary limit for a hyperbolic system describing ferromagnetism, SIAM J. Math. Anal., 34, (2002), 315-340.
J. L. Joly, G. Metivier, J. Rauch, Global solvability of the anharmonic oscillator model from nonlinear optics, SIAM J. Math. Anal., 27, (1996), 905-913.
J. L. Joly, G. Metivier, J. Rauch, Global solutions to Maxwell’s equations in a ferromagnetic medium, Ann. Inst. Henry Poincaré, 1, (2000), 307-340.
G. A. Kriegsmann, Microwave heating of dispersive media, SIAM J. Appl. Math., 53, 4, (1993), 655-669.
F. Midwinter, Zernicke, Applied Nonlinear Optics, Wiley, 1972.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York 1983.
A. Sauter, Nonlinear Optics, Wiley, 1983.
C.Weber, A local compactness theorem for Maxwell’s equations, Math. Methods Appl. Sci. 2, (1980), pp. 12-25.
N.Weck, Maxwell’s boundary value problem on Riemannian manifolds with nonsmooth boundaries, J. Math. Anal. Appl. 46, (1974), pp. 410-437.
A. Visintin, On Landau-Lifschitz equation for ferromagnetism, Japan J. of Appl. Math., 2, No. 1, 69-84.
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