リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「WELL-POSEDNESS AND PARABOLIC SMOOTHING EFFECT FOR HIGHER ORDER SCHRO¨ DINGER TYPE EQUATIONS WITH CONSTANT COEFFICIENTS」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

WELL-POSEDNESS AND PARABOLIC SMOOTHING EFFECT FOR HIGHER ORDER SCHRO¨ DINGER TYPE EQUATIONS WITH CONSTANT COEFFICIENTS

Tanaka, Tomoyuki 大阪大学 DOI:10.18910/87488

2022.04

概要

In this paper, we consider the Cauchy problem of a class of higher order Schr¨odinger type equations with constant coefficients. By employing the energy inequality, we show the L2 well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property.

参考文献

[1] T. Akhunov: A sharp condition for the well-posedness of the linear KdV-type equation, Proc. Amer. Math. Soc. 142 (2014), 4207–4220.

[2] H. Chihara: The initial value problem for Schro¨dinger equations on the torus, Int. Math. Res. Not. (2002), 789–820.

[3] S. Doi: Remarks on the Cauchy problem for Schro¨dinger-type equations, Comm. Partial Differential Equa- tions 21 (1996), 163–178.

[4] A. Gru¨nrock: On the hierarchies of higher order mKdV and KdV equations, Cent. Eur. J. Math. 8 (2010), 500–536.

[5] N. Hayashi: The initial value problem for the derivative nonlinear Schro¨dinger equation in the energy space, Nonlinear Anal. 20 (1993), 823–833.

[6] N. Hayashi and T. Ozawa: On the derivative nonlinear Schro¨dinger equation, Phys. D 55 (1992), 14–36.

[7] J.K. Hunter, M. Ifrim, D. Tataru and T.K. Wong: Long time solutions for a Burgers-Hilbert equation via a modified energy method, Proc. Amer. Math. Soc. 143 (2015), 3407–3412.

[8] W. Ichinose: Some remarks on the Cauchy problem for Schro¨dinger type equations, Osaka J. Math. 21 (1984), 565–581.

[9] K. Kajitani: The Cauchy problem for Schro¨dinger type equations with variable coeflcients, J. Math. Soc. Japan 50 (1998), 179–202.

[10] C.E. Kenig and D. Pilod: Local well-posedness for the KdV hierarchy at high regularity, Adv. Differential Equations 21 (2016), 801–836.

[11] C.E. Kenig, G. Ponce and L. Vega: Higher-order nonlinear dispersive equations, Proc. Amer. Math. Soc. 122 (1994), 157–166.

[12] S. Kwon: On the fifth-order KdV equation: local well-posedness and lack of uniform continuity of the solution map, J. Differential Equations 245 (2008), 2627–2659.

[13] S. Mizohata: On some Schro¨dinger type equations, Proc. Japan Acad. Ser. A Math. Sci. 57 (1981), 81–84.

[14] S. Mizohata: On the Cauchy problem, Academic Press, Orlando, 1985.

[15] R. Mizuhara: The initial value problem for third and fourth order dispersive equations in one space dimen- sion, Funkcial. Ekvac. 49 (2006), 1–38.

[16] M. Schwarz Jr.: The initial value problem for the sequence of generalized Korteweg-de Vries equations, Adv. in Math. 54 (1984), 22–56.

[17] J. Takeuchi: On the Cauchy problem for some non-Kowalewskian equations with distinct characteristic roots, J. Math. Kyoto Univ. 20 (1980), 105–124.

[18] S. Tarama: On the H∞-wellposed Cauchy problem for some Schro¨dinger type equations, Mem. Fac. Engrg. Kyoto Univ. 55 (1993), 143–153.

[19] S. Tarama: L2-well-posed Cauchy problem for fourth-order dispersive equations on the line, Electron. J. Differential Equations 2011, No. 168, 11pp.

[20] K. Tsugawa: Local well-posedness of derivative Schro¨dinger equations on the torus, preprint.

[21] K. Tsugawa: Parabolic smoothing effect and local well-posedness of fifth order semilinear dispersive equa- tions on the torus, arXiv:1707.09550.

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る