Critical exponent for a nonlinear wave equation with damping

Journal of Differential Equations

Volumn 174, Issue 2, 2001, Pages 464-489

  Todorova, Grozdena ^a   Yordanov, Borislav ^b  

^a UNIVERSITY OF TENNESSEE   (United States)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001626801     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3933     Document Type: Article

References (22)

1. R. Agemi, K. Kubota, and H. Takamura, On certain integral equations related to nonlinear wave equations, Hokkaido Math. J. 23 (1994), 241-276.
2. p, C. R. Acad. Sci. Paris Sér. I 306 (1988), 359-364.
3. p, J. Differential Equations 82 (1989), 98-108.
4. 1+α, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 13 (1990), 109-124.
5. V. Georgiev, H. Lindblad, and C. Sogge, Weighted srichards estimates and global existence for semilinear wave equation, Amer. J. Math. 119 (1997), 1291-1319.
6. R. Glassey, Existence in the large for □u = f(u) in two dimensions, Math. Z. 178 (1981), 233-261.
7. Y. Han and A. Milani, "On the Diffusion Phenomenon of Quasilinear Hyperbolic Waves in Low Space Dimensions," preprint, 1998.
8. L. Hsiao and T. Liu, Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservations with damping, Comm. Math. Phys. 143 (1992), 599-605.
9. F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math. 28 (1979), 235-268.
10. R. Kanwal, "Generalized Functions: Theory and Technique," Academic Press, New York, 1983.
11. 1 + α, Discr. and Cont. Dynamical Systems 1 (1995), 503-520.
12. H. Lindblad and C. Sogge, On the Small-power Semilinear Wave Equations, preprint, 1995.
13. A. Matsumura, On the asymptotic behaviour of solutions of semilinear wave equations, Publ. RIMS Kyoto Univ. 121 (1976), 169-189; (1998), 191-196.
14. A. Matsumura, On the asymptotic behaviour of solutions of semilinear wave equations, Publ. RIMS Kyoto Univ. 121 (1976), 169-189; (1998), 191-196.
15. M. Nakao and K. Ono, Existence of global solutions to the cauchy problem for the semilinear dissipative wave equations, Math. Z. 214 (1993), 325-342.
16. F. Olver, "Asymptotics and Special Functions," Academic Press, New York, 1974.
17. T. Sideris, Ph.D. thesis, Indiana University, Bloomington, 1981.
18. T. Sideris, Nonexistence of global solutions to semilinear wave equations in high dimensions, J. Differential Equations 52 (1984), 378-406.
19. W. Strauss, Nonlinear scattering theory at low energy, J. Func. Anal. 41 (1981), 110-133.
20. W. Strauss, "Nonlinear wave equations," C.B.M.S. Lecture Notes, Vol. 73, American Math. Soc., Providence, RI, 1989.
21. D. Tataru, Strichartz Estimates in the Hyperbolic Space and Global Existence for the Semilinear Wave Equation, preprint, 1998.
22. Y. Zhou, Cauchy problem for semilinear wave equations in four space dimensions with small initial data, J. Partial Differential Equations 8 (1995), 135-144.