Stability of global gevrey solution to weakly hyperbolic equations

Chinese Annals of Mathematics. Series B

Volumn 18, Issue 1, 1997, Pages 1-14

  Reissig, M ^a   Yagdjian, K ^b  

^a TU BERGAKADEMIE FREIBERG   (Germany)

^b Institute of Mathematics National Academy of Sciences of Armenia   (Armenia)

Author keywords

Gevrey functions; Global solvability; Life span of solutions; Quasilinear weakly hyperbolic equations; Stability

Indexed keywords

EID: 21744457165     PISSN: 02529599     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. 2, in: Partial Differential Equations and the Calculus of Variations, vol.1, Essays in Honor of Enrico de Giorgi, Progress in Non-linear Differential Equations and their applications, Birkhäuser (1989), 331-353.
2. D'Ancona, P. & Spagnolo, S., On the life span of the analytic solutions to quasilinear weakly hyperbolic equations, Indiana Univ. Math. Journal, 40:1 (1991), 71-99.
3. Ivrii, V. & Petkov, V., Necessary conditions for well-posedness of the Cauchy problem for nonstrictly hyperbolic equations (in Russian), Usp. Math. Nauk, 29:5 (1974), 3-70.
4. Ivrii, V., Linear hyperbolic equations, in: Linear Partial Differential Equations, 197-4 (Modern Mathematical Problems: Fundamental Trends) (in Russian), 33 (1988), 157-247.
5. Kajitani, K., Local solution of Cauchy problem for nonlinear hyperbolic systems in Gevrey classes, Hokkaido Math. J., 12 (1983), 434-460.
6. Klainerman, S., Global existence for nonlinear wave equations, Comm. Pure Appl. Math., 33 (1980), 43-101.
7. Li Ta-Tsien & Chen Yunmei, Global classical solutions for nonlinear evolution equations, Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Publishing House, 45 (1991), 209.
8. Nersesian, A., On a Cauchy problem for degenerate hyperbolic equations of second order (in Russian), Dokl. Akad. Nauk SSSR, 166 (1966), 1288-1291.
9. Ponce, G., Racke, R., Sideris, T. C. & Titi, E. S., Global stability of large solutions to the 3d Navier-Stokes equations (accepted for publication in Comm. Math. Phys.).
10. Racke, R., Lectures on nonlinear evolution equations, Aspects of Mathematics, Vieweg, Braunschweig/Wiesbaden, 19 (1992), 259.
11. Reissig, M. A: Yagdjian, K., On the Cauchy problem for quasilinear weakly hyperbolic equations with time degeneration, Journal of Contemporary Mathematical Analysis, 28:2 (1993), 31-50.
12. Reissig, M. & Yagdjian, K., Levi conditions and global Gevrey regularity for the solutions of quasilinear weakly hyperbolic equations, Math.Nachr., 178 (1996), 285-307.
13. Shinkai, K., Stokes multipliers and a weakly hyperbolic operator, Comm. Partial Diff. Equ., 16: 4-5 (1991), 667-682.
14. Spagnolo, S., Analytic regularity of the solutions of a semi-linear weakly hyperbolic equation, Ricerche di Matematica, Suppl, 36 (1987), 193-202.
15. Taniguchi, K. & Shinkai, K., Fundamental solution for a degenerate hyperbolic operator in Gevrey classes, Publ. RIMS Kyoto Univ., 28 (1992), 169-205.
16. Yagdjian, K., The Cauchy problem for weakly hyperbolic equations in classes of Gevrey functions (in Russian), Izv. Akad. Nauk Arm. SSR, Matematika, 13 (1978), 3-22.
17. Yagdjian, K., Necessary conditions for the correctness of the Cauchy problem for operators with multiple characteristics, Comm. Partial Diff. Equ., 19:1-2 (1994), 1-25.