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\(L^p\)-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I. (German) Zbl 0318.35054

MSC:
35L05 Wave equation
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
35L15 Initial value problems for second-order hyperbolic equations
42B05 Fourier series and coefficients in several variables
35B45 A priori estimates in context of PDEs
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References:
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[2] Brenner, P., Thomée, V., Wahlbin, L. B.: Besov spaces and applications to difference methods for initial value problems. Lecture Notes in Mathematics Nr. 434, Springer Berlin-Heidelberg-New York 1975 · Zbl 0294.35002
[3] Browder, F. E.: On the spectral theory of elliptic differential operators I. Math. Ann.142, 22-130 (1961) · Zbl 0104.07502
[4] Calderón, A. P.: Lebesgue spaces of differentiable functions and distributions. In: Proceedings of Symposia in Pure Mathematics vol. IV, Partial Differential Equations (Berkeley 1960), pp. 33-49. Providence: American Mathematical Society 1961
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[11] Pecher, H.: Globale klassische Lösungen nichtlinearer Wellengleichungen für höhere Raumdimensionen. Nachr. Akad. Wiss. II. math.-phys. Kl. Nr.14, 221-232 (1975). · Zbl 0317.35058
[12] Strichartz, R. S.: Convolutions with kernels having singularities on a sphere. Trans. Amer. math. Soc.148, 461-471 (1970) · Zbl 0199.17502
[13] Strichartz, R. S.: A priori estimates for the wave equation and some applications. J. functional Analysis5, 218-235 (1970) · Zbl 0189.40701
[14] von Wahl, W.: Klassische Lösungen nichtlinearer Wellengleichungen im Großen. Math. Z.112, 241-279 (1969) · Zbl 0177.36602
[15] von Wahl, W.: Über nichtlineare Wellengleichungen mit zeitabhängigem elliptischen Hauptteil. Math. Z.142, 105-120 (1975) · Zbl 0299.35064
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[17] von Wahl, W.: Regular solutions of initial-boundary value problems for linear and nonlinear wave equations II. Math. Z.142, 121-130 (1975) · Zbl 0301.35063
[18] von Wahl, W.:L p -decay rates for homogeneous wave-equations. Math. Z.120, 93-106 (1971) · Zbl 0212.44201
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