Asymptotic expansions of the solutions to a class of quasilinear hyperbolic initial value problems

Atsushi YOSHIKAWA

doi:10.2969/jmsj/04720227

Atsushi YOSHIKAWA

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 2 Pages 227-252

DOI https://doi.org/10.2969/jmsj/04720227

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Published: 1995 Received: May 27, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Hunter, A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves, II: Several space variables, Stud. Appl. Math., 75 (1986), 187-226.
2) J.-L. Joly, J. Metivier and J. Rauch, Remarques sur l'optique géometrique non linéairemultidimensionnelle, Sém. E.D.P., 1990-1991, Ecole Polytechnique.
3) A. Majda, Nonlinear geometric optics for hyperbolic systems of conservation laws, In Oscillation theory, computation, and methods of compactness, IMA, vol. 2, Springer, New York, 1986, pp. 115-165.
4) A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Appl. Math. Ser., 53, Springer, Berlin-Heidelberg-New York, 1984.
5) A. Majda, The interaction of nonlinear analysis and modern applied mathematics, Proc. ICM 1990, vol. 1, The Mathematical Society of Japan, Springer, Tokyo-Berlin-Heidelberg-New York-London-Hong Kong-Barcelona-Budapest, 1991, pp. 175-191.
6) S. Schochet, Fast singular limits of hyperbolic PDEs, (preprint 1992).
7) A. Yoshikawa, Solutions containing a large parameter of a quasi-linear hyperbolic system of equations and their non-linear geometric optics approximation, Trans. Amer. Math. Soc., 340 (1993), 103-126.
8) A. Yoshikawa, Quasilinear oscillations and geometric optics, Adv. Math. Sci. Appl., 4 (1994), 381-398.
9) A. Yoshikawa, Quasilinear geometric optics approximation, Lecture Notes in Math., 1540, Springer, 1993, pp. 403-413.

Right : [1] J. Hunter, A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves, II: Several space variables, Stud. Appl. Math., 75 (1986), 187-226.
[2] J. -L. Joly, J. Metivier and J. Rauch, Remarques sur l'optique géometrique non linéaire multidimensionnelle, Sém. E. D. P., 1990-1991, Ecole Polytechnique.
[3] A. Majda, Nonlinear geometric optics for hyperbolic systems of conservation laws, In Oscillation theory, computation, and methods of compactness, IMA, vol. 2, Springer, New York, 1986, pp. 115-165.
[4] A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Appl. Math. Ser., 53, Springer, Berlin-Heidelberg-New York, 1984.
[5] A. Majda, The interaction of nonlinear analysis and modern applied mathematics, Proc. ICM 1990, vol. 1, The Mathematical Society of Japan, Springer, Tokyo-Berlin-Heidelberg-New York-London-Hong Kong-Barcelona-Budapest, 1991, pp. 175-191.
[6] S. Schochet, Fast singular limits of hyperbolic PDEs, (preprint 1992).
[7] A. Yoshikawa, Solutions containing a large parameter of a quasi-linear hyperbolic system of equations and their non-linear geometric optics approximation, Trans. Amer. Math. Soc., 340 (1993), 103-126.
[8] A. Yoshikawa, Quasilinear oscillations and geometric optics, Adv. Math. Sci. Appl., 4 (1994), 381-398.
[9] A. Yoshikawa, Quasilinear geometric optics approximation, Lecture Notes in Math., 1540, Springer, 1993, pp. 403-413.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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