Notes on geometric aspects of effectively hyperbolic critical points when the characteristic roots are real on one side of time

Tatsuo Nishitani

doi:10.3792/pjaa.100.008

July 2024 Notes on geometric aspects of effectively hyperbolic critical points when the characteristic roots are real on one side of time

Tatsuo Nishitani

Proc. Japan Acad. Ser. A Math. Sci. 100(7): 37-42 (July 2024). DOI: 10.3792/pjaa.100.008

Abstract

Geometric aspects of effectively hyperbolic critical points on time $t=0$ are discussed assuming that the characteristic roots are real on one side of time $t$, namely time is positive. In particular, we aim to elucidate the differences in the geometric aspects of effectively hyperbolic critical points on time $t=0$ when the characteristic roots are real on both the positive and negative sides of time.

References

1.

L. Hörmander, The Cauchy problem for differential equations with double characteristics, J. Anal. Math., 32 (1977), 118-196.L. Hörmander, The Cauchy problem for differential equations with double characteristics, J. Anal. Math., 32 (1977), 118-196.

2.

V. Ivrii and V. M. Petkov, Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Uspehi Mat. Nauk, 29 (1974), no. 5, 3-70.V. Ivrii and V. M. Petkov, Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations, Uspehi Mat. Nauk, 29 (1974), no. 5, 3-70.

3.

V. Ivrii, Sufficient conditions for regular and completely regular hyperbolicity, Trudy Moskov. Mat. Obšč., 33 (1975), 3-65.V. Ivrii, Sufficient conditions for regular and completely regular hyperbolicity, Trudy Moskov. Mat. Obšč., 33 (1975), 3-65.

4.

K. Kajitani and T. Nishitani, The hyperbolic Cauchy problem, Lecture Notes in Math., 1505, Springer-Verlag, Berlin, 1991, pp. 71-167.K. Kajitani and T. Nishitani, The hyperbolic Cauchy problem, Lecture Notes in Math., 1505, Springer-Verlag, Berlin, 1991, pp. 71-167.

5.

T. Nishitani, A note on reduced forms of effectively hyperbolic operators and energy integrals, Osaka J. Math., 21 (1984), no. 4, 843-850.T. Nishitani, A note on reduced forms of effectively hyperbolic operators and energy integrals, Osaka J. Math., 21 (1984), no. 4, 843-850.

6.

T. Nishitani, Local energy integrals for effectively hyperbolic operators. I, II, J. Math. Kyoto Univ., 24 (1984), no. 4, 623-658, 659-666.T. Nishitani, Local energy integrals for effectively hyperbolic operators. I, II, J. Math. Kyoto Univ., 24 (1984), no. 4, 623-658, 659-666.

7.

T. Nishitani, The Cauchy problem for operators with triple effectively hyperbolic characteristics: Ivrii's conjecture, J. Anal. Math., 149 (2023), no. 1, 167-237.T. Nishitani, The Cauchy problem for operators with triple effectively hyperbolic characteristics: Ivrii's conjecture, J. Anal. Math., 149 (2023), no. 1, 167-237.

Citation Download Citation

Tatsuo Nishitani "Notes on geometric aspects of effectively hyperbolic critical points when the characteristic roots are real on one side of time," Proceedings of the Japan Academy, Series A, Mathematical Sciences 100(7), 37-42, (July 2024). https://doi.org/10.3792/pjaa.100.008

Published: July 2024

Access the abstract

JOURNAL ARTICLE
6 PAGES

DOWNLOAD PDF + SAVE TO MY LIBRARY