Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation

João-Paulo Dias; Mário Figueira

Bollettino dell'Unione Matematica Italiana (2000)

  • Volume: 3-B, Issue: 3, page 739-750
  • ISSN: 0392-4041

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Dias, João-Paulo, and Figueira, Mário. "Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation." Bollettino dell'Unione Matematica Italiana 3-B.3 (2000): 739-750. <http://eudml.org/doc/195984>.

@article{Dias2000,
author = {Dias, João-Paulo, Figueira, Mário},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {break-down of strong solutions; weak entropy solutions; compensated compactness},
language = {eng},
month = {10},
number = {3},
pages = {739-750},
publisher = {Unione Matematica Italiana},
title = {Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation},
url = {http://eudml.org/doc/195984},
volume = {3-B},
year = {2000},
}

TY - JOUR
AU - Dias, João-Paulo
AU - Figueira, Mário
TI - Blow-up and global existence of a weak solution for a sine-Gordon type quasilinear wave equation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2000/10//
PB - Unione Matematica Italiana
VL - 3-B
IS - 3
SP - 739
EP - 750
LA - eng
KW - break-down of strong solutions; weak entropy solutions; compensated compactness
UR - http://eudml.org/doc/195984
ER -

References

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  2. DIAS, J. P.- FIGUEIRA, M., On the blow-up of the solutions of a quasilinear wave equation with a semilinear source term, Math. Meth. Appl. Sci., 19 (1996), 1135-1140. Zbl0857.35085MR1409543
  3. DIAS, J. P.- FIGUEIRA, M., Existence d'une solution faible pour une équation d'ondes quasi-linéaires avec un terme de source semi-linéaire, C.R. Acad. Sci. Paris, 322, Série I (1996), 619-624. Zbl0857.35084MR1386463
  4. DIAS, J. P.- FIGUEIRA, M.- SANCHEZ, L., Formation of singularities for the solutions of some quasilinear wave equations, Equa. dérivées part. et applic., Articles dédiés à J. L. Lions, Gauthier-Villars, Paris, 1998, 453-460. Zbl0921.35111MR1648233
  5. DIPERNA, R. J., Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal., 82 (1983), 27-70. Zbl0519.35054MR684413
  6. DOUGLIS, A., Some existence theorems for hyperbolic systems of partial differential equations in two independent variables, Comm. Pure Appl. Math., 5 (1952), 119-154. Zbl0047.09101MR52666
  7. HARTMAN, P.- WINTER, A., On hyperbolic differential equations, Amer. J. Math., 74 (1952), 834-864. Zbl0048.33302MR51413
  8. LAX, P. D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys., 5 (1964), 611-613. Zbl0135.15101MR165243
  9. MAJDA, A., Compressible fluid flow and systems of conservation laws in several space variables, Applied Math. Sciences, Vol. 53, Springer, 1984. Zbl0537.76001MR748308
  10. MURAT, F., Compacité par compensation, Ann. Scuola Norm. Sup. Pisa, 5 (1978), 489-507. Zbl0399.46022MR506997
  11. RAUCH, J., Partial differential equations, Graduate texts in Mathematics, Vol. 128, Springer, 1991. Zbl0742.35001MR1223093
  12. SMOLLER, J., Shock waves and reaction-diffusion equations, Grund. math. Wissenschaften, Vol. 258, Springer, 1983. Zbl0508.35002MR688146
  13. TARTAR, L., Compensated compactness and applications to partial differential equations, Heriot-Watt Sympos., IV, Pitman, New York, 1979, 136-212. Zbl0437.35004MR584398

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