Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in H3

Discrete and Continuous Dynamical Systems

Volumn 5, Issue 4, 1999, Pages 753-763

  Wang, Baoxiang ^a  

^a HEBEI UNIVERSITY   (China)

Author keywords

Klein Gordon equations; Scattering of solutions

Indexed keywords

EID: 0347752526     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1999.5.753     Document Type: Article

References (23)

1. J. Bergh J and J. Löfström, Interpolation Spaces, Springer-Verlag, 1976
2. P. Brenner, On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations, Math. Z. 186 (1984), 383-391.
3. P. Brenner, On scattering and everywhere-defined scattering operators of nonlonear Klein-Gordon equations, J. Diff. Eqns. 56 (1985), 310-344.
4. 3, Nonlinear Anal. TMA 14 (1990), 807-836.
5. J. Ginibre and G. Velo, Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations, Ann. Inst. H. Poincare. Phys. Theor. 43 (1985), 399-442.
6. J. Ginibre and G. Velo, Generalized Strichartz inequalities for the wave equation, J. Funct. Anal. 133 (1995), 50-68.
7. L.V. Kapitanskii, Weak and yet weak solutions of semilinear wave equations, Comm. Partial Diff. Equations 19 (1994), 1629-1676.
8. M. Keel and T. Tao, End point Strichartz estimates, Amer. J. of Math. 120 (1998), 955-980.
9. H. Lindblad and C.D. Sogge, On existence and scattering with minimal regularity for semilinear wave equations, J.of Funct. Anal. 130 (1995), 357-426.
10. C. S. Morawetz and W. A. Strauss, Decay and scattering of solutions of a nonlinear relativistic wave equation, Comm. Pure Appl. Math. 25 (1972), 1-31.
11. H. Pecher, Nonlinear small data scattering for the wave and Klein-Gordon equations, Math.Z. 185 (1984) 261-270.
12. H. Pecher, Low energy scattering for nonlinear Klein-Gordon equations, J. of Funct. Anal. 63 (1985), 101-122.
13. W. Strauss, Nonlinear scattering theory at low energy, J. of Funct. Anal. 42 (1981), 110-133 and 43 (1981), 281-293 .
14. W. Strauss, Nonlinear scattering theory at low energy, J. of Funct. Anal. 42 (1981), 110-133 and 43 (1981), 281-293 .
15. W. Strauss, Nonlinear Wave Equations, Lecture Notes, Vol. 73 AMS, Providence, RI. 1989
16. M. Tsutsumi and N. Hayashi, Scattering of solutions of nonlinear Klein-Gordon equations in higher space dimensions, in Nonlinear PDE'83 Proceeding, Lecture Notes in Numerical and Applied Analysis, Vol.6, North-Holland, Amsterdam
17. H. Triebel, Function Space Theory, Birkhäuser-Verlag, 1983
18. Wang Baoxiang, Potential Banach function spaces and nonlinear wave equations , Doctoral thesis, Inst. of Appl. Phys. and Comput. Math. Beijing, 1993, 1-224.
19. 3, Nonlinear Analysis, TMA, 31 (1998), 173-187.
20. Wang Baoxiang, Classical global solutions for nonlinear Klein-Gordon-Schrödinger equations, Math. Meth. in the Appl. Sci. 20 (1997) 599-616
21. 3, Advance in Math. (China) 25 (1996) 471-472, and J. Partial Diff. Eqs., 11 (1998), 173-192.
22. 3, Advance in Math. (China) 25 (1996) 471-472, and J. Partial Diff. Eqs., 11 (1998), 173-192.
23. Wang Baoxiang, Bessel (Riesz) potentials on Banach function spaces and their applications I, Theory, Acta Math. Sinica (N.S.) 14 (1998), 327-340.