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Das Verhalten globaler Lösungen nichtlinearer Wellengleichungen für große Zeiten. (German) Zbl 0269.35059


MSC:

35L05 Wave equation
35L60 First-order nonlinear hyperbolic equations
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References:

[1] Courant, R., Hilbert, D.: Methoden der mathematischen Physik I. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0156.23201
[2] Courant, R., Hilbert, D.: Methoden der mathematischen Physik II. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0161.29402
[3] Hadamard, J.: Lectures on Cauchy’s problem in linear partial differential equations. New Haven-London: Yale University Press-Oxford University Press 1923 · JFM 49.0725.04
[4] Jörgens, K.: Das Anfangswertproblem im Großen für eine Klasse nichtlinearer Wellengleichungen. Math. Z.77, 295-308 (1961) · Zbl 0111.09105
[5] Morawetz, C. S., Strauss, W. A.: Decay and scattering of solutions of a nonlinear relativistic wave equation. Commun. Pure appl. Math.25, 1-31 (1972) · Zbl 0228.35055
[6] Sather, J.: The existence of a global classical solution of the initial-boundary value problem for ?u+u 3=f Arch. rat. Mech. Analysis22, 292-307 (1966) · Zbl 0141.28802
[7] Segal, I. E.: Nonlinear semi-groups. Ann. of Math. II. Ser.78, 339-364 (1963) · Zbl 0204.16004
[8] Segal, I. E.: Dispersion for non-linear relativistic equations II. Ann. sci. Ecole norm. sup., IV. Sér.1, 459-497 (1968) · Zbl 0179.42302
[9] Strauss, W. A.: Decay and asymptotics for ?u=F(u). J. functional Analysis2, 409-457 (1968) · Zbl 0182.13602
[10] Wahl, W. von: Klassische Lösungen nichtlinearer Wellengleichungen im Großen. Math. Z.112, 241-279 (1969) · Zbl 0177.36602
[11] Wahl, W. von: Über die klassische Lösbarkeit des Cauchy-Problems für nichtlineare Wellengleichungen bei kleinen Anfangswerten und das asymptotische Verhalten der Lösungen. Math. Z.114, 281-299 (1970) · Zbl 0186.17001
[12] Wahl, W. von: Some decay-estimates for nonlinear wave equations. J. functional Analysis9, 490-495 (1972) · Zbl 0229.35054
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