Levi conditions and global Gevrey regularity for the solutions of quasilinear weakly hyperbolic equations

Mathematische Nachrichten

Volumn 178, Issue , 1996, Pages 285-307

  Reissig, Michael ^a   Yagdjian, Karen ^b  

^a TU BERGAKADEMIE FREIBERG   (Germany)

^b INSTITUTE OF ORGANIC CHEMISTRY   (Armenia)

Author keywords

Cone of dependence; Gevrey spaces; Global regularity; Local existence result; Weakly hyperbolic equations

Indexed keywords

EID: 0009318355     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19961780114     Document Type: Article

References (18)

1. ALINHAC, S., and MÉTIVIER, G.: Propagation de l'Analyticité des Solutions des Systèmes Hyperboliques Non-Linéaires, Inv. Math., 75 (1984), 189-203
2. D'ANCONA, P., and MANFRIN. R.: The Cauchy Problem in Abstract Gevrey Spaces for a Non-linear Weakly Hyperbolic Equation of Second Order, Preprints di Matematica, n. 145, October 1992, Scuola Normale Superiore, Pisa, 1-17.
3. D'ANCONA, P., and SPAGNOLO. S.: On the Life Span of the Analytic Solutions of Quasilinear Weakly Hyperbolic Equations, Indiana Univ. Math. J., 40-1 (1991), 71-99
4. GEVREY, M.: Sur les Équations aux Dérivées du Type Parabolique, J. Math. Pures Appl., 9 (1913), 305-471
5. GLAESER, G.: Racine Carrée d'une Fonction Différentiable, Ann. Inst. Fourier, 13 (1963), 203-210
6. IVRII, V., and 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
7. IVRII, V.; Conditions for Well-Posedness in Gevrey Classes of the Cauchy Problem for Hyperbolic Equations with Characteristics of Variable Multiplicity (in Russian), Sib. Mat. Zh., 17-6 (1976), 1256-1270
8. IVRII, V.: Well-Posedness in Gevrey Classes of the Cauchy Problem for Nonstrictly Hyperbolic Operators (in Russian), Izv. Vyssh. Uch. Zaved., 2(1978), 26-35
9. IVRII, V.: Linear Hyperbolic Equations, in: Linear Partial Differential Equations, 197-4 (Modern Mathematical Problems: Fundamental Trends) (in Russian), 33 (1988), 157-247
10. IVRII, V.: Linear Hyperbolic Equations, in: Linear Partial Differential Equations, 197-4 (Modern Mathematical Problems: Fundamental Trends) (in Russian), 33 (1988), 157-247
11. KAJITANI, K.: Local Solution of Cauchy Problem for Nonlinear Hyperbolic Systems in Gevrey Classes, Hokkaido Math. J., 12 (1983), 434-460
12. LERAY, J., and OHYA, Y.: Systémes Nonlineaires Hyperboliques Nonstrictes, Math. Ann., 70 (1967), 167-205
13. MIZOHATA, S.: Analyticity of Solutions of Hyperbolic Systems with Analytic Coefficients, Comm. Pure Appl. Math., 15 (1961), 547-559
14. MIZOHATA, S.: The Theory of Partial Differential Equations, Cambridge Univ. Press, Cambridge, 1973
15. e Série, 107 (1983), 113-138
16. OLEINIK, O.: On the Cauchy Problem for Weakly Hyperbolic Equations, Comm. Pure Appl. Math., 23 (1970), 569-586
17. SPAGNOLO, S.: Analytic Regularity of the Solutions of a Semi-Linear Weakly Hyperbolic Equation, Ricerche di Matematica, Suppl., 36 (1987), 193-202
18. YAGDJIAN, K.: Necessary Conditions for the Correctness of the Cauchy Problem for Operators with Multiple Characteristics, Comm. Partial Diff. Equat. 19 No. 1&2 (1994), 1-25