HARUHISA ISHIDA
| Division of General Education（Graduate School of Informatics and Engineering） | Associate Professor |
| Division of General Education（School of Informatics and Engineering ） | Associate Professor |
| Department of Computer and Network Engineering | Associate Professor |
| Cluster I (Informatics and Computer Engineering) | Associate Professor |
Researcher Information
Research Activity Information
Paper
- On second order weakly hyperbolic equations and the ultradifferentiable classes
Fumihiko Hirosawa; Haruhisa Ishida
Journal of Differential Equations, ACADEMIC PRESS INC ELSEVIER SCIENCE, 255, 7, 1437-1468, 01 Oct. 2013, We consider second order weakly hyperbolic equations with time dependent coefficients in the ultradifferentiable classes. Our main purpose of the present paper is an investigation the relation between the classes of the functions to be well-posed and the following properties of the coefficients: the order of degeneration, stabilization to a monotonic function and their smoothness in the ultradifferentiable classes. (C) 2013 Elsevier Inc. All rights reserved.
Scientific journal, English - On asymptotic behaviour of solutions to linear differential systems with variable coeffcients via characteristic numbers
Haruhisa Ishida; Hyung Ju Lee
Funkcialaj Ekvacioj, KOBE UNIV, DEPT MATHEMATICS, 53, 3, 359-379, Dec. 2010, We treat the system of linear differential equations with variable coefficients and examine its asymptotic behaviour via several characteristic numbers. Especially, we give a few conditions to admit the solution with polynomial order in terms of second exponent. Moreover, we establish an estimate of the solution to linear nonhomogeneous system by an inequality of Wazewski type, which leads to one of the Lyapunov exponent as well.
Scientific journal, English - Oscillatory properties for semilinear degenerate hyperbolic equations of second order
Haruhisa Ishida; Yasuo Yuzawa
Journal of Mathematical Analysis and Applications, ACADEMIC PRESS INC ELSEVIER SCIENCE, 356, 2, 624-632, 15 Aug. 2009, We consider three kind of oscillatory properties of the solutions to semilinear degenerate hyperbolic equations. Several sufficient conditions for the oscillation or non-oscillation are presented. In particular, they give us the positivity of the solutions for semilinear hyperbolic equations degenerating at initial point in one space dimension. Moreover we establish a few oscillatory conditions for the solutions of the mixed problem reduced to in one space dimension. (C) 2009 Elsevier Inc. All rights reserved.
Scientific journal, English - Levi conditions to the gevrey well-posedness for hyperbolic operators of higher order
Haruhisa Ishida
Kyoto Journal of Mathematics, DUKE UNIV PRESS, 49, 1, 173-191, 2009, We consider a class of linear higher order hyperbolic equations with a single degenerate point. We give sufficient conditions in order for the Cauchy problem to be well-posed in Gevrey classes and in the C-infinity class.
Scientific journal, English - Well-posedness of the cauchy problem in gevrey classes for some weakly hyperbolic equations of higher order
Ferruccio Colombini; Haruhisa Ishida
Journal d'Analyse Mathematique, 90, 13-25, 2003, This article is devoted to the study of the Cauchy problem in Gevrey classes for some higher order weakly hyperbolic equations with time-dependent coefficients and without lower order terms.
Scientific journal - On a sharp Levi condition in Gevrey classes for some infinitely degenerate hyperbolic equations and its necessity
Haruhisa Ishida; Karen Yagdjian
Publications of the Research Institute for Mathematical Sciences, 38, 2, 265-287, Aug. 2002
Scientific journal - On the Cauchy problem for finitely degenerate hyperbolic equations of second order
Ferruccio Colombini; Haruhisa Ishida; Nicola Orrú
Arkiv for Matematik, 38, 2, 223-230, Oct. 2000, This paper is devoted to the study of the Cauchy problem in C∞ and in the Gevrey classes for some second order degenerate hyperbolic equations with time dependent coefficients and lower order terms satisfying a suitable Levi condition.
Scientific journal
MISC
- On second order weakly hyperbolic equations and the ultradifferentiable classes
Fumihiko Hirosawa; Haruhisa Ishida
We consider second order weakly hyperbolic equations with time dependent coefficients in the ultradifferentiable classes. Our main purpose of the present paper is an investigation the relation between the classes of the functions to be well-posed and the following properties of the coefficients: the order of degeneration, stabilization to a monotonic function and their smoothness in the ultradifferentiable classes. (C) 2013 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE, Oct. 2013, JOURNAL OF DIFFERENTIAL EQUATIONS, 255, 7, 1437-1468, English, 0022-0396, WOS:000322092900003 - On second order weakly hyperbolic equations and the ultradifferentiable classes
2013, Journal of Differential Equations, 255, 7, 1437-1468 - On Asymptotic Behaviour of Solutions to Linear Differential Systems with Variable Coefficients via Characteristic Numbers
Haruhisa Ishida; Hyung-Ju Lee
We treat the system of linear differential equations with variable coefficients and examine its asymptotic behaviour via several characteristic numbers. Especially, we give a few conditions to admit the solution with polynomial order in terms of second exponent. Moreover, we establish an estimate of the solution to linear nonhomogeneous system by an inequality of Wazewski type, which leads to one of the Lyapunov exponent as well., KOBE UNIV, DEPT MATHEMATICS, Dec. 2010, FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 53, 3, 359-379, English, 0532-8721, WOS:000285497600002 - 退化双曲型方程式に対する振動定理について
2010, 愛媛大学工学部, 7 - On asymptotic behavior of solutions to linear differential systems with variable coefficients via characteristic numbers
2010, Funkcialaj Ekvacioj (Serio Internacia), 53, 3, 359-379 - Oscillatory properties for semilinear degenerate hyperbolic equations of second order
Haruhisa Ishida; Yasuo Yuzawa
We consider three kind of oscillatory properties of the solutions to semilinear degenerate hyperbolic equations. Several sufficient conditions for the oscillation or non-oscillation are presented. In particular, they give us the positivity of the solutions for semilinear hyperbolic equations degenerating at initial point in one space dimension. Moreover we establish a few oscillatory conditions for the solutions of the mixed problem reduced to in one space dimension. (C) 2009 Elsevier Inc. All rights reserved., ACADEMIC PRESS INC ELSEVIER SCIENCE, Aug. 2009, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 356, 2, 624-632, English, 0022-247X, WOS:000266339700020 - 新しい特性数による変数係数線形微分方程式系の解の挙動について
2009, 日本大学理工学部数学教室 - Levi conditions to the Gevrey well-posedness for hyperbolic operators of higher order
Haruhisa Ishida
We consider a class of linear higher order hyperbolic equations with a single degenerate point. We give sufficient conditions in order for the Cauchy problem to be well-posed in Gevrey classes and in the C(infinity) class., KINOKUNIYA CO LTD, 2009, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 49, 1, 173-191, English, 0023-608X, WOS:000267269200009 - Levi conditions to the Gevrey well-posedness for hyperbolic operators of higher order
2009, Journal of Mathematics of Kyoto University, 49, 1, 173-191 - Oscillatory properties for semilinear degenerate hyperbolic equations of second order
2009, Journal of Mathematical Analysis and Applications, 356, 2, 624-632 - Colombini-Taglialatela 型の Levi 条件の改良への試み
2008, 山口大学大学院理工学研究科数理科学教室, 1 - 多項式位数の解をもつ線形常微分方程式系の性質について
2008, 東京都立産業技術高等専門学校, 7 - Asymptotic behaviour of solutions to systems of linear ODEs with variable coefficients via characteristic numbers
2008, Department of Mathematics, Faculty of Science, Kyoto University, 13 - An endeavor to improve the Levi condition of Colombini and Taglialatela type
2008, Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, 1 - Asymptotic behaviour of solutions to systems of linear ODEs with variable coefficients via characteristic numbers
2008, Department of Mathematics, Faculty of Science, Kyoto University, 13 - 荷重関数による高階双曲型方程式に対するレビ条件
2007, 東海大学理学部数学教室 - コロンビーニ・タリアラテラによるレビ条件の変種
2007, 愛媛大学工学部, 13 - 半線形退化双曲型方程式に対する振動性質
2007, 京都大学大学院理学研究科数学教室, 1 - 半線形退化双曲型方程式に対する振動性質Ｉ
2007, 東海大学 山中湖セミナーハウス, 17 - Levi conditions for higher order hyperbolic equations by weight functions
2007, Department of Mathematics, Faculty of Science, Tokai University - A variant of the Levi condition by Colombini and Taglialatela
2007, Faculty of Technology, Ehime University, 13 - Oscillatory properties for semilinear degenerate hyperbolic equations
2007, Department of Mathematics, Faculty of Science, Kyoto University, 1 - Oscillatory properties for semilinear degenerate hyperbolic equations I
2007, Seminar House of Tokai University at Yamanakako, 17 - Ｓ．ベルンシュタインの定理と関連した解析関数の挙動
2006, 京都大学大学院理学研究科数学教室, 8 - Asymptotic of analytic functions related with S. Bernstein's theorem
2006, Department of Mathematics, Graduate School of Science, Kyoto University, 8 - 技術革新の普及を表すマンスフィールドモデルの拡張について
2005, 宮崎大学教育文化学部, 2 - On some extension of E. Mansfield's model on the spread of technological innovation
2005, Faculty of Education and Culture, Miyazaki University, 2 - 発展方程式に対する初期値問題の C∞ 適切性
2004, 東海大学理学部数学教室 - C∞ wellposedness of the Cauchy problem for evolution equations
2004, Department of Mathematics, Faculty of Science, Tokai University - Well-posedness of the Cauchy problem in Gevrey classes for some weakly hyperbolic equations of higher order
F Colombini; H Ishida
This article is devoted to the study of the Cauchy problem in Gevrey classes for some higher order weakly hyperbolic equations with time-dependent coefficients and without lower order terms., SPRINGER, 2003, JOURNAL D ANALYSE MATHEMATIQUE, 90, 13-25, English, 0021-7670, WOS:000226077700002 - Well-posedness of the Cauchy problem in Gevrey classes for some weakly hyperbolic equations of higher order
2003, Journal d'Analyse Mathematique, 90, 13-25 - On a sharp Levi condition in Gevrey classes for some infinitely degenerate hyperbolic equations and its necessity
H Ishida; K Yagdjian
KYOTO UNIV, Aug. 2002, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 38, 2, 265-287, English, 0034-5318, WOS:000179206800003 - On a sharp Levi condition in Gevrey classes for some infinitely degenerate hyperbolic equations and its necessity
2002, Publications of the Research Institute for Mathematical Sciences, Kyoto University, 38, 2, 265-287 - On the Cauchy problem for finitely degenerate hyperbolic equations of second order
F Colombini; H Ishida; N Orru
This paper is devoted to the study of the Cauchy problem in C-infinity and in the Gevrey classes for some second order degenerate hyperbolic equations with time dependent coefficients and lower order terms satisfying a suitable Levi condition., INST MITTAG LEFFLER, Oct. 2000, ARKIV FOR MATEMATIK, 38, 2, 223-230, English, 0004-2080, WOS:000174336700002 - The initial value problem for some degenerate hyperbolic equations of second order in Gevrey classes
2000, Funkcialaj Ekvacioj (Serio Internacia), 43, 1, 71-85 - On the Cauchy problem for finitely degenerate hyperbolic equations of second order
2000, Arkiv fo"r Matematik, 38, 2, 223-230 - The Cauchy problem for weakly hyperbolic equations of second order
Ishida, Haruhisa
Institute of Mathematics, University of Tsukuba, Jun. 1999, Tsukuba journal of mathematics, 23, 1, 1-26, Japanese, 0387-4982, 110000027613, AA00874643 - The Cauchy problem for weakly hyperbolic equations of second order
1999, Tsukuba Journal of Mathematics, 23, 1, 1-26 - Global smooth solutions of semilinear weakly hyperbolic equations with logarithmic nonlinearity
1998, Ehime Univ., 74-81 - Global smooth solutions of semilinear weakly hyperbolic equations with logarithmic nonlinearity
1998, Ehime Univ., 74-81 - On uniform well-posedness of the abstract Cauchy problem
Haruhisa Ishida
Institute of Mathematics, University of Tsukuba, Dec. 1997, Tsukuba journal of mathematics, 21, 3, 617-628, English, 0387-4982, 110000027544, AA00874643 - On uniform well-posedness of the abstract Cauchy problem
1997, Tsukuba Journal of Mathematics, 21, 3, 617-628
Books and other publications
Research Themes
- 対角化による双曲型方程式の解のエネルギー評価法
2012 - Energy estimates for solutions of hyperbolic equations via refined diagonalizations
2012 - 退化双曲型方程式に対する振動理論
基礎科学研究
2007 - Oscillation Theory for Degenerate Hyperbolic Equations
Basic Science Research Program
2007 - 非線形弱双曲型方程式に対する大域可解性
- 弱双曲型方程式に対する初期値問題の適切性
- Global solvability for nonlinear weakly hyperbolic equations
- Well-posedness of the Cauchy problem for weakly hyperbolic equations
