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Global, small amplitude solutions to nonlinear evolution equations. (English) Zbl 0509.35009

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35L70 Second-order nonlinear hyperbolic equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:
[1] Klainerman, Comm. Pure Appl. Math. 33 pp 43– (1980)
[2] Long time behavior of the solution to nonlinear equations, preprint.
[3] Strauss, J. Funct. Anal. 41 pp 110– (1981)
[4] Marshall, J. Math. Pure Appl. 59 pp 417– (1980)
[5] Matsumura, Proc. Japan Acad. 55 (1979)
[6] Shatah, Amer. Math. Soc. 2 (1981)
[7] Pecher, I, Math. Z. 150 pp 159– (1976)
[8] Strichatz, Trans. Amer. Math. Soc. 148 pp 461– (1970)
[9] von Wahl, Math. Z. 120 pp 93– (1971)
[10] Global existence of small solutions to nonlinear evolution equations, preprint.
[11] Long Time Stability of Solutions of Nonlinear Evólution Equations, Ph.D. Thesis, New York Univ., 1982.
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