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Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux

S. Alinhac

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

  • page 1-12

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Alinhac, S.. "Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux." Séminaire Équations aux dérivées partielles (Polytechnique) (1992-1993): 1-12. <http://eudml.org/doc/112066>.

@article{Alinhac1992-1993,
author = {Alinhac, S.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {singularity formation; blow-up mechanism; small data; unfolded system; Burgers' equation},
language = {fre},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux},
url = {http://eudml.org/doc/112066},
year = {1992-1993},
}

TY - JOUR
AU - Alinhac, S.
TI - Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1992-1993
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - fre
KW - singularity formation; blow-up mechanism; small data; unfolded system; Burgers' equation
UR - http://eudml.org/doc/112066
ER -

References

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  1. [1] Alinhac S.Une solution approchée en grands temps des équations d'Euler compressibles axisymétriques en dimension deux, Comm. in PDE, 17 (3 et 4), (1992), 447-490. Zbl0755.35089MR1163433
  2. [2] Alinhac S.Approximation près du temps d'explosion des solutions d'équations d'ondes quasi-linéaires en dimension deux Preprint, Paris-Sud/ Orsay (1992). Zbl0870.35063MR1163433
  3. [3] Alinhac S.Temps de vie et comportement explosif des solutions d'équations d'ondes quasi-linéaires en dimension deux I et II, Preprint, Paris-Sud/ Orsay (1992 et 1993). 
  4. [4] Di Perna R. et Majda A.The validity of geometrical optics for weak solutions of conservation lawsComm. Math. Phys.98 (1985), 313-347. Zbl0582.35081MR788777
  5. [5] Friedlander G.On the radiation field of pulse solutions of the wave équation I, II, Proc. Roy. Soc. A, 269 (1962), 53-65 et 279 (1964), 386-394. Zbl0117.43904MR142888
  6. [6] Hörmander L.The lifespan of classical solutions of non linear hyperbolic equations, Mittag Leffler report n° 5 (1985). Zbl0632.35045
  7. [7] Hörmander L.Non linear hyperbolic differential equations, Lectures, (1986-87). 
  8. [8] John F.Non linear wave equations, formation of singularitiesPitcher lectures in the Math. Sciences AMS (1990). Zbl0716.35043MR1066694
  9. [9] John F.Solutions of quasilinear wave equations with small initial data ; the third phase, non linear hyperbolic equations Proceedings, Bordeaux (1988), Lecture notes in mathematics 1402, Springer Verlag, 155-184. Zbl0694.35012MR1033282
  10. [10] John F.Blow up of radial solutions of utt = c2(ut)Δ u in three space dimensionsMath. Aplicada e Comp.4 (1985), 3-18. Zbl0597.35082
  11. [11] John F.Existence for large times of strict solutions of non linear wave equations in three space dimensions for small initial data, Comm. in PureAppl. Math.40, (1987), 79-109. Zbl0662.35070MR865358
  12. [12] John F. et Klainerman S.Almost global existence to non linear wave equations in three space dimensionsComm. Pure Appl. Math.37 (1984) 443-55. Zbl0599.35104MR745325
  13. [13] Klainerman S.Weighted L∞ and L1 estimates for solutions to the classical wave equation in three space dimensionsComm. Pure Appl. Math37 (1984) 269-88. Zbl0583.35068
  14. [14] Klainerman S.Uniform decay estimates and the Lorentz invariance of the classical wave equationComm. Pure Appl. Math.38 (1985) 321-332. Zbl0635.35059MR784477
  15. [15] Majda A.Compressible fluid flows and systems of conservation laws SpringerAppl. Math. Sc.53 (1984). Zbl0537.76001
  16. [16] Majda A. et Rosales R.Resonantly interacting weakly non linear hyperbolic waves I. A single space variable, Stud. Appl. Math.71 (1984) 149-179. Zbl0572.76066MR760229
  17. [17] Wasow W.Asymptotic expansions for ordinary differential equationsKrieger, New York (1976). Zbl0644.34003MR460820

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