The Lax-Mizohata theorem for nonlinear Cauchy problems

Communications in Partial Differential Equations

Volumn 26, Issue 7-8, 2001, Pages 1367-1384

  Wakabayashi, Seiichiro ^a  

^a UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21544465603     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-100106137     Document Type: Article

References (8)

1. Lax, P.D. Asymptotic Solutions of Oscillatory Initial Value Problems. Duke Math. J. 1957, 24, 624-646.
2. Mizohata, S. Some Remarks on the Cauchy Problem. J. Math. Kyoto Univ. 1961, 1, 109-127.
3. Ivrii, V. Ja.; Petkov, V.M. Necessary Conditions for the Cauchy Problem for Non-Strictly Hyperbolic Equations to be Well-posed, Uspehi Mat. Nauk 1974, 29 (5), 3-70.
4. (Russian; English translation in Russian Math. Surveys.)
5. Yagdjian, K. A Note on Lax-Mizohata Theorem for Quasilinear Equations. Comm. in Partial Differential Equations 1998, 23, 1111-1122.
6. Yagdjian, K. The Lax-Mizohata Theorem for Nonlinear Gauge Invariant Equations, to appear.
7. Choquet-Bruhat, Y. Ondes Asymptotiques Et Approchées Pour Les Systèmes D'équations Aux Dérivées Partielles Non Linéaires. J. Math. Pure Appl. 1969, 48, 117-158.
8. Hunter, J.; Keller, J. Weakly Nonlinear High Frequency Waves, Comm. Pure Appl. Math. 1983, 36, 547-569.