×

Blow-up for quasi-linear wave equations in three space dimensions. (English) Zbl 0453.35060


MSC:

35L70 Second-order nonlinear hyperbolic equations
35L10 Second-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] The Cauchy problem for quasi-linear symmetric hyperbolic systems, Archive for Rat. Mech. Analysis, 1974 –75, pp. 57–58.
[2] Hughes, Archives Rat. Mech. Analysis 63-4 pp 273– (1976)
[3] John, Comm. Pure Appl. Math. 29 pp 649– (1976)
[4] A functional analytic approach to existence and uniqueness of solutions to some nonlinear Cauchy problems, preprint.
[5] Knops, Arch. Rational Mech. Anal. 55 pp 52– (1974)
[6] Improperly posed problems in partial differential equations, Regional Conference Series in Appl. Math. 22, 1975, SIAM. · doi:10.1137/1.9781611970463
[7] Globale klassische Lösungen nichtlinearer Wellengleichungen für höhere Raumdimensionen, Nachr. Akad. Wiss. Göttingen Math. Phys., Kl. II, 1975, pp. 221–232.
[8] Pecher, Math. Z. 150 pp 159– (1976)
[9] Manuscripta Math. 20 pp 227– (1977)
[10] Existenzsätze für reguläre Lösungen semilinearer Wellengleichungen, Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl. II, 1979, pp. 129–151. · Zbl 0431.35014
[11] and , Global classical solutions of nonlinear wave equations, preprint.
[12] Finite-time blow-up for solutions of nonlinear wave equations, preprint. · Zbl 0438.35045
[13] Kato, Comm. Pure Appl. Math. 33 (1980)
[14] John, Manuscripta Math. 28 pp 235– (1979)
[15] Klainerman, Comm. Pure Appl. Math. 33 pp 43– (1980)
[16] Long time behaviour of solutions to nonlinear evolution equation, preprint.
[17] Lax, Regional Conference Series in Applied Mathematics 11 (1973)
[18] John, Comm. Pure Appl. Math. 27 pp 377– (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.