Characterization of hyperbolic operators with the coefficients of the principal part depending only on the time variable for which the Cauchy problem is well-posed
| Project/Area Number |
16K05222
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | University of Tsukuba |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2016-04-01 – 2021-03-31
|
| Project Status |
Completed (Fiscal Year 2020)
|
| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 双曲型作用素 / コーシー問題 / Ｃ∞適切性 / 超局所解析 / 双曲型方程式 / 適切性 / 偏微分方程式 |
|---|
| Outline of Final Research Achievements |
In the preceding researches I obtained sufficient conditions of C∞ well-posedness of the Cauchy problem for higher-order hyperbolic operators with double characteristics satisfying the conditions that the coefficients of the principal parts are real analytic functions of the time variable. And I showed that these sufficient conditions are also necessary when the space dimension is less than 3 or the coefficients of the principal parts are semi-algebraic functions ( e.g., polynomials ) of the time variable.
I also considered the Cauchy problem for higher-order hyperbolic operators with triple characteristics whose coefficients are real analytic functions of the time variable. And I obtained similar results concerning the characterization of C∞ well-posedness.
|
| Academic Significance and Societal Importance of the Research Achievements |
双曲型作用素に対するコーシー問題の C∞適切性の特徴付けは、偏微分方程式論における主要なテーマの１つであり、これまでに多くの研究があるが、未だ満足のいく結果は得られていないのが現状である。報告者が、主部の係数が時間変数にのみに依存する特別な枠組みではあるが、２重特性的である場合に C∞適切性の特徴付けを与えたことは、今後のこの分野の研究・発展に貢献するものと期待される。また３重特性的な場合を扱うために、subprincipal symbol を一般化して、sub-sub-principal symbol を初めて定義して、係数が時間変数のみに依存する場合に、C∞適切性の特徴付けを与えた。
|
Report
(6 results)
Research Products
(7 results)
