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
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.