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


35L70 Second-order nonlinear hyperbolic equations
35L10 Second-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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[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.
[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)
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