The study of the entropy solutions of one dimensional 2 times 2 systems of conservation laws
| Project/Area Number |
16K17610
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Niigata University |
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Principal Investigator |
Ohwa Hiroki 新潟大学, 自然科学系, 准教授 (10549158)
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| Research Collaborator |
Sasaki Yoshimasa
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 実解析 / 保存則方程式 / 非線形現象 / 解析学 / 関数方程式論 / 実関数論 / 数理物理 |
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| Outline of Final Research Achievements |
In order to find clues to solve the existence and uniqueness of the entropy solutions to the initial value problem for one dimensional 2×2 systems of conservation laws, we proved the existence and uniqueness of the entropy solutions to the initial value problems for a scalar conservation law of similar form to the Temple type, with a flux function which is a smooth function multiplied by a discontinuous coefficient on the spatial location, and for a scalar conservation law with a flux function which is (more generally) discontinuous with respect to the unknown function. Moreover, we proved the continuous dependence in the sense of L＾1 on the initial value and the flux of the entropy solutions to the initial value problems for a scalar conservation law (with smooth flux).
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| Academic Significance and Societal Importance of the Research Achievements |
数理科学の様々な分野において, 各種物理量の時間発展はそれら物理量の保存則方程式から導かれる複数の非線形偏微分方程式（保存則方程式系）で記述される. 保存則方程式系の研究は１９５０年代から多くの研究者によって行われてきたが, その系統的な結果は未だに得られていない. こうしたことから, 保存則方程式系の研究は今後の発展に期待されており, 学術的に大きな意義を持つ研究課題であると言える.このような学術的背景の中で，本研究課題では，保存則方程式系の初期値問題の一意可解性問題の解決への糸口を探ることを目的として研究を行い，ある一定の成果を得ることができた．
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Report
(4 results)
Research Products
(6 results)
