文献
J-GLOBAL ID:200902276586622460
整理番号:09A0112122 準定数係数基本部を有する双曲線演算子用のコーシー問題について
On the Cauchy Problem for Hyperbolic Operators with Nearly Constant Coefficient Principal Part
- [1] Atiyah, M. F., Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150.
- [2] Chazarain, J., Operateurs hyperboliques à caracteristiques de multiplicité constante, Ann. Inst. Fourier, <b>24</b> (1974), 173-202.
- [3] Dunn, J. L., A sufficient condition for hyperbolicity of partial differential operators with constant coefficient principal part, Trans. Amer. Math Soc., 201 (1975), 315-327.
- [4] Flaschka, H. and Strang, G., The correctness of the Cauchy problem, Advances in Math., 6 (1971), 347-379.
- [5] Gårding, G., Linear hyperbolic partial differential equations with constant coefficients, Acta Math., <b>85</b> (1951), 1-62.
- [6] Hörmander, L., <i>The Analysis of Linear Partial Differential Operators I</i>, Springer, Berlin-Heidelberg-New York-Tokyo, 1983.
- [7] Hörmander, L., <i>The Analysis of Linear Partial Differential Operators III</i>, Springer, Berlin-Heidelberg-New York-Tokyo, 1985.
- [8] Ivrii, V. Ja. and Petkov, V., Necessary condition for the Cauchy problem for non-strictly hyperbolic equations to be well-posed, Uspehi Mat. Nauk, 29 (1974), 3-70. (Russian; English translation in Russian Math. Surveys.)
- [9] Kajitani, K. and Wakabayashi, S., Microhyperbolic operators in Gevrey classes, Publ. Res. Inst. Math. Sci., 25 (1989), 169-221.
- [10] Kajitani, K. and Wakabayashi, S., Microlocal a priori estimates and the Cauchy problem II, Japan. J. Math., 20 (1994), 1-71.
- [11] Kajitani, K. and Wakabayashi, S., The Cauchy problem for a class of hyperbolic operators with double characteristics, Funkcial. Ekvac., 39 (1996), 235-307.
- [12] Kajitani, K., Wakabayashi, S. and Nishitani, T., The Cauchy problem for hyperbolic operators of strong type, Duke Math. J., 75 (1994), 353-408.
- [13] Kajitani, K., Wakabayashi, S., and Yagdjian, K., The <i>C</i><sup>∞</sup>-well posed Cauchy problem for hyperbolic operators dominated by time functions, Japan J. Math., <b>30</b> (2004), 283-348.
- [14] Kumano-go, H., Pseudo-Differential Operators, MIT Press, Cambridge, 1982.
- [15] Mandai, T., Generalized Levi conditions for weakly hyperbolic equations—An attempt to treat the degeneracy with respect to the space variables—, Publ. Res. Inst. Math. Sci., <b>22</b> (1986), 1-23.
- [16] Treves, F., Introduction to Pseudodifferential and Fourier Integral Operators II, Plenum Press, New York, 1980.
- [17] Wakabayashi, S., The Cauchy problem for operators with constant coefficient hyperbolic principal part and propagation of singularities, Japan J. Math., 6 (1980), 179-228.
- [18] Wakabayashi, S., Singularities of solutions of the Cauchy problems for operators with nearly constant coefficient hyperbolic principal part, Comm. Partial Differential Equations, 8 (1983), 347-406.
- [19] Wakabayashi, S., Generalized Hamilton flows and singularities of solutions of the hyperbolic Cauchy problem, Taniguchi Symp., HERT, Kyoto 1984, Kinokuniya, Tokyo, pp. 415-423.
- [20] Wakabayashi, S., Remarks on hyperbolic polynomials, Tsukuba J. Math., 10 (1986), 17-28.
前のページに戻る