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Global existence of small solutions to nonlinear evolution equations. (English) Zbl 0518.35046


MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35B20 Perturbations in context of PDEs
34G20 Nonlinear differential equations in abstract spaces
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References:

[1] Klainerman, S., Global existence for nonlinear wave equations, Comm. Pure Appl. Math., 33, 43-101 (1980) · Zbl 0405.35056
[2] S. Klainerman, Long time behaviour of solution to nonlinear evolution equations, preprint.; S. Klainerman, Long time behaviour of solution to nonlinear evolution equations, preprint. · Zbl 0581.35052
[3] Marshall, B.; Strauss, W. A.; Wainger, S., \(L^p\) − \(L^q\) estimates for the Klein-Gordon equation, J. Math. Pures Appl., 59, 417-440 (1980) · Zbl 0457.47040
[4] strauss, W. A., Nonlinear scattering theory, (Scattering Theory in Mathematical Physics (1974), Reidel: Reidel Dordrecht), 53-78 · Zbl 0297.35062
[5] Strauss, W. A., Nonlinear invariant wave equations, (Invariant Wave Equations (Erice, 1977). Invariant Wave Equations (Erice, 1977), Lecture Notes in Physics No. 73 (1978), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York), 197-249
[6] Strauss, W. A., Nonlinear scattering theory at low energy, J. Funct. Anal., 41, 110-133 (1981) · Zbl 0466.47006
[7] Strichartz, R. S., Convolutions with kernels having singularities on a sphere, Trans. Amer. Math. Soc., 148, 461-471 (1970) · Zbl 0199.17502
[8] S. Klainerman and Gustavo Ponce, Global small amplitude solutions to nonlinear evolution equations, preprint.; S. Klainerman and Gustavo Ponce, Global small amplitude solutions to nonlinear evolution equations, preprint. · Zbl 0509.35009
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