Global classical solutions of nonlinear wave equations. (English) Zbl 0457.35059


35L70 Second-order nonlinear hyperbolic equations
35L75 Higher-order nonlinear hyperbolic equations
35B45 A priori estimates in context of PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
Full Text: DOI EuDML


[1] Bergh, J., Löfström, J.: Interpolation spaces. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0344.46071
[2] Brenner, P.: On the Existence of Global Smooth Solutions of Certain Semi-Linear Hyperbolic Equations. Math. Z.167, 99-135 (1979) · Zbl 0395.35064
[3] Browder, F.E.: On the Spectral Theory of Elliptic Differential Operators I. Math. Ann.142, 22-130 (1961) · Zbl 0104.07502
[4] Heinz, E., Wahl, W. von: Zu einem Satz von F.E. Browder über nichtlineare Wellengleichungen. Math. Z.141, 33-45 (1975) · Zbl 0289.35076
[5] Pecher, H.:L p -Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. Math. Z.150, 159-183 (1976) · Zbl 0347.35053
[6] Pecher, H.: Ein nichtlinearer Interpolationssatz und seine Anwendung auf nichtlineare Wellengleichungen. Math. Z.161, 9-40 (1978) · Zbl 0384.35039
[7] Tanabe, H.: Equations of Evolution. London, San Francisco, Melbourne: Pitman 1979 · Zbl 0417.35003
[8] Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. Amsterdam: North Holland 1978 · Zbl 0387.46032
[9] Wahl, W. von: Klassische Lösungen nichtlinearer Wellengleichungen im Großen. Math. Z.112, 241-279 (1969) · Zbl 0177.36602
[10] Wahl, W. von: Nichtlineare Wellengleichungen mit zeitabhängigem elliptischen Hauptteil. Math. Z.142, 105-120 (1975) · Zbl 0299.35064
[11] Wahl, W. von: Regular Solutions of Initial-Boundary Value Problems for Linear and Nonlinear Wave-Equations II. Math. Z.142, 121-130 (1975) · Zbl 0301.35063
[12] Wahl, W. von: Analytische Abbildungen und semilineare Differentialgleichungen in Banachräumen. Nachr. Ak. d. Wiss. Göttingen, II. Mathematisch-Physikalische Klasse, 153-200 (1979) · Zbl 0433.34047
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