Nonresonance and global existence of prestressed nonlinear elastic waves

Annals of Mathematics

Volumn 151, Issue 2, 2000, Pages 849-874

  Sideris, Thomas C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034399662     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121050     Document Type: Article

References (17)

1. R. AGEMI, Global existence of nonlinear elastic waves, Hokkaido University Preprint Series, #463, July 1999.
2. D. CHRISTODOULOU, Global solutions of nonlinear hyperbolic equations for small data, Comm. Pure Appl. Math. 39 (1986), 267-282.
3. F. JOHN, Blow-up for quasi-linear wave equations in three space dimensions. Comm. Pure Appl. Math. 34 (1981), 29-51.
4. _, Formation of singularities in elastic waves, Lecture Notes in Physics 195 Springer-Verlag, New York (1984), 194-210.
5. _, Almost global existence of elastic waves of finite amplitude arising from small initial disturbances, Comm. Pure Appl. Math. 41 (1988), 615-666.
6. _, Nonlinear Wave Equations, Formation of Singularities (Pitcher Lectures, Lehigh Univ., April, 1980), University Lectures Series 2, A.M.S., Providence, RI, 1990.
7. _, Nonlinear Wave Equations, Formation of Singularities (Pitcher Lectures, Lehigh Univ., April, 1980), University Lectures Series 2, A.M.S., Providence, RI, 1990.
8. F. JOHN and S. KLAINERMAN, Almost global existence to nonlinear wave equations in three space dimensions, Comm. Pure Appl. Math. 37 (1984), 443-455.
9. S. KLAINERMAN, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math. 38 (1985), 321-332.
10. _, The null condition and global existence to nonlinear wave equations, Lect. in Appl. Math. 23 (1986), 293-326.
11. S. KLAINERMAN and T. SIDERIS, On almost global existence for nonrelativistic wave equations in 3D, Comm. Pure Appl. Math. 49 (1996), 307-321.
12. R. OGDEN, Nonlinear Elastic Deformations, E. Horwood Series: Mathematics and its Applications, Halsted Press, New York (1984).
13. T. SIDERIS, Global behavior of solutions to nonlinear wave equations in three dimensions, Comm. P.D.E. 8 (1983), 1291-1323.
14. _, The null condition and global existence of nonlinear elastic waves, Invent. Math. 123 (1996), 323-342.
15. _, Uniform decay estimates for some hyperbolic equations, Proc. Conf. in Honor of W. Strauss (May 1998), to appear.
16. T. SIDERIS and S.-Y. TU, Global existence for systems of nonlinear wave equations in 3D with multiple speeds, preprint.
17. A. S. TAHVILDAR-ZADEH, Relativistic and nonrelativistic elastodynamics with small shear strains, Ann. Inst. H. Poincaré - Phys. Théor. 69 (1998), 275-307.