On the profiles of nonlinear geometric optics

J. L. Joly; G. Métivier; J. Rauch

Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993)

  • page 1-14

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Joly, J. L., Métivier, G., and Rauch, J.. "On the profiles of nonlinear geometric optics." Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993): 1-14. <http://eudml.org/doc/112060>.

@article{Joly1992-1993,
author = {Joly, J. L., Métivier, G., Rauch, J.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {profile equation; high-frequency solutions},
language = {eng},
pages = {1-14},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {On the profiles of nonlinear geometric optics},
url = {http://eudml.org/doc/112060},
year = {1992-1993},
}

TY - JOUR
AU - Joly, J. L.
AU - Métivier, G.
AU - Rauch, J.
TI - On the profiles of nonlinear geometric optics
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1992-1993
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 14
LA - eng
KW - profile equation; high-frequency solutions
UR - http://eudml.org/doc/112060
ER -

References

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  1. [G] J. Glimm, Solutions in the large for nonlinear systems of conservation laws, Comm. Pure Appl. Math.18(1965), 685-715. Zbl0141.28902MR194770
  2. [GL] J. Glimm and P.D. Lax, Decay of solutions of systems of nonlinear hyperbolic hyperbolic conservation laws, Memoirs A.M.S.101, 1970. Zbl0204.11304
  3. [Je] A. Jeffrey, Breakdown of the solution to a completely exceptional system of hyperbolic equations, J. Math. Anal. Appl.45(1974) 375-381. Zbl0281.35058MR333472
  4. [Jo] F. John, Formation of singularities in one-dimensional nonlinear wave propagation, Comm. Pure Appl. Math.37(1974) 377-405. Zbl0302.35064MR369934
  5. [JMR1] J-L. Joly, G. Metivier, and J. Rauch, Resonant one dimensional nonlinear geometric optics, Journal of Functional Analysis, to appear. Zbl0851.35023MR1220985
  6. [JMR2] J-L. Joly, G. Metivier, and J. Rauch.Formal and rigorous nonlinear high frequency hyperbolic waves, pp. 121-143 in Proceedings of Varenna Conference on Nonlinear Hyperbolic Equations and Field Theory, M.K. Murthy and S. Spagnolo eds., Pitman Research Notes in Math. 1992 Zbl0824.35077MR1175206
  7. [JMR3] J-L. Joly, G. Metivier, and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J., to appear Zbl0815.35066MR1219817
  8. [JMR4] J-L. Joly, G. Metivier. and J. Rauch, Unbounded variation amplification for 3x3 systems of conservation laws, preprint. 
  9. [H] J. Hunter, Strongly nonlinear hyperbolic waves, in Notes on Numerical Fluid Dynamics Vol.24, Nonlinear Hyperbolic Equations, eds. J. Ballman and R. Jeltsch, Vieweg, Braunschweig, 1989. Zbl0689.35083MR991371
  10. [L] P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math.10(1957), 537-566. Zbl0081.08803MR93653
  11. [MR] A. Majda and R. Rosales, Resonantly interacting weakly nonlinear hyperbolic waves I, a single space variable. Stud.Appl.Math.71(1984)149-179. Zbl0572.76066MR760229
  12. [P] R. Pego, Some explicit resonating waves in weakly nonlinear gas dynamics, Stud. Appl. Math.71(1984)263-270. Zbl0669.76104MR975486
  13. [R] J. Rauch, BV estimates fail for most quasilinear hyperbolic systems in dimension greater than one, Comm.Math.Phys.106(1986)484-489. Zbl0619.35073MR859822
  14. [S] S. Schochet, Resonant nonlinear geometric optics for weak solutions of conservation laws, preprint. Zbl0856.35080MR1297667

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