The Initial Value Problem for Third and Fourth Order Dispersive Equations in One Space Dimension

Funkcialaj Ekvacioj

Volumn 49, Issue 1, 2006, Pages 1-38

  Mizuhara, Ryuichiro ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

Dispersive equations; Initial value problem; Pseudodifferential calculus; Smoothing effect; Well posedness

Indexed keywords

EID: 44849113804     PISSN: 05328721     EISSN: None     Source Type: Journal    
DOI: 10.1619/fesi.49.1     Document Type: Article

References (14)

1. Chihara, H., The initial value problem for Schrödinger equations on torus, Int. Math. Res. Not., 15 (2002), 789–820.
2. Doi, S.-I., On the Cauchy problem for Schrödinger type equations and the regularity of solutions, J. Math. Kyoto Univ., 34 (1994), 319–328.
3. Doi, S.-I., Remarks on the Cauchy problem for Schrödinger-type equations, Commun. Partial Differential Equations, 21 (1996), 163–178.
4. Doi, S.-I., Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J., 82 (1996), 679–706.
5. Hörmander, L., The analysis of linear partial differential operators III, Springer-Verlag, 1985.
6. Hoshiro, T., Decay and regularity for dispersive equations with constant coefficients, J. Anal. Math., 91 (2003), 211–230.
7. Ichinose, W., On L2 well posedness of the Cauchy problem for Schrödinger type equations on the Riemannian manifold and the Maslov theory, Duke Math. J., 56 (1988), 549–588.
8. Ichinose, W., A note on the Cauchy problem for Schrödinger type equations on the Riemannian manifold, Math. Japon., 35 (1990), 205–213.
9. Kumano-go, H., Pseudodifferential operators, MIT Press, Cambridge, 1981.
10. Mizohata, S., On the Cauchy problem, Academic Press, 1985.
11. Takeuchi, J., A necessary condition for the well-posedness of the Cauchy problem for certain class of evolution equations, Proc. Japan Acad., 50 (1974), 133–137.
12. Takeuchi, J., Some remarks on my paper “On the Cauchy problem for some non-kowalewskian equations with distinct characteristic roots”, J. Math. Kyoto Univ., 24 (1984), 741–754.
13. Tarama, S., On the wellposed Cauchy problem for some dispersive equations, J. Math. Soc. Japan, 47 (1995), 143–158.
14. Tarama, S., Remarks on L2-wellposed Cauchy problem for some dispersive equations, J. Math. Kyoto Univ., 37 (1997), 757–765.