New developments in mathematical analysis of spatio-temporal nonuniform dynamics in quasilinear hyperbolic-parabolic conservation laws

拟线性双曲-抛物线守恒定律时空非均匀动力学数学分析新进展

• 批准号: 20H00118
• 负责人: 隠居 良行
• 金额: $ 28.7万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2020
• 资助国家: 日本
• 起止时间: 2020-04-01 至 2024-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-20H00118/
• 关键词: 準線形双曲放物型方程式系; 圧縮Navier-Stokes方程式; 分岐; 安定性; ダイナミクス; 圧縮性Navier-Stokes方程式

隠居と西田は無限層状領域における塩分濃度の変動を考慮に入れた非圧縮性熱対流方程式に対する人工圧縮近似方程式を考察し，人工Mach数ゼロの極限でそのHopf分岐が非圧縮熱対流方程式のHopf分岐解に収束することを証明した．また，隠居は圧縮性Taylor渦の空間非周期的摂動に対する線形化安定性解析を完成させた．西田はRayleigh-Benard 熱対流の二次元問題のロール型の解について，Rayleigh 数を上げる時，現在の解析では扱えない定常解から周期解を経て周期倍分岐を起こして、chaoticな挙動に至る路を計算機援用解析として見出した．こうして非線形偏微分方程式の場合にもchaosに至る経路に周期倍分岐のシナリオがある事を示した．川島は双曲型平衡則系モデルに対し，構造保存型差分解の時間大域存在を示した．また，記憶型拡散項を持つ対称双曲系の解の減衰評価を示した．さらに，指数関数の記憶核の場合に，記憶型消散項を持つ空間1次元対称双曲系の解の漸近形を求めた．前川は緩和双曲型線形偏微分方程式について研究を行い，エネルギー消散評価と係数行列の代数的な条件を一般的な枠組みで与えた．福本は浅水流の速度不連続面の不安定性に関して不連続面を境に深さが不連続に変わる効果を調べ，深さが等しいときに臨界フルード数が極小値2.82をとることを証明した．鈴木は流体力学における基礎方程式の時間大域解の漸近挙動を解析した．主な成果としては，摂動半空間においてNavie-Stokes方程式の定常解の存在と安定性を，半空間においてBoltzmann方程式の時間周期解の存在と安定性を証明した.

In Nishida, there is no limit on the field of distribution. The test is applied to the non-linear flow equation. The artificial Mach data limit is limited to the Hopf bifurcation equation. The Hopf bifurcation solution is valid. The dynamic stability analysis of non-periodic Taylor traffic in space is completed. The two-dimensional problem of Rayleigh-Benard flow in Westfield is a two-dimensional solution, and the Rayleigh number is on the rise. Now, in the analysis of the constant solution of the cycle, the periodic bifurcation of the cycle, the double bifurcation of the cycle, and the calculation of the chaotic movement to the road, the calculation machine is used to solve the problem. The equation of non-linear partial differential equations is used to solve the equation of periodic bifurcation from the chaos to the road. The results show that the hyperbolic equilibrium system of the Sichuan railway is a hyperbolic equilibrium system. There is an indication in the large time domain of the differential decomposition of the preservation type. in this case, the memory-type dispersion term holds that the hyperbolic system is called the hyperbolic system to solve the decay problem, and the exponential value is in combination. The memory-type dissipation term is called the solution of the hyperbolic system of the first degree in space to solve the approximation problem of the hyperbolic system. Maegawa and hyperbolic partial differential equations In terms of the conditions of the algebra of the number of numbers, the conditions of the algebra are generally related to the conditions of the algebra. Fukamoto shallow current velocity is not uneasy, qualitative analysis, non-contact, non-contact, non-contact and non-contact. There is a very small number of applications in the field of deep engineering, such as 2.82, the basic equations of fluid mechanics, the time-domain solution of the equations of near motion, the analysis of the results, the stability of the steady solution of the Navie-Stokes equation, and so on. There is a stability analysis for the periodic solution of the Boltzmann equation in half-space.

项目成果

Stability of Benney--Luke Line Solitary Waves in 2 Dimensions

Benney稳定性--二维卢克线孤立波

• DOI: 10.1137/19m1253848
• 发表时间: 2020
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Mizumachi Tetsu;Shimabukuro Yusuke
• 通讯作者: Shimabukuro Yusuke

An example of thermal convection in the horizontal layer with non-uniform heat supply

供热不均匀的水平层热对流示例

• 发表时间: 2022
• 作者: Taguchi Hirokazu;Murakami Yuta;Koga Akihisa;Nasu Joji;Yukari Matsuzuka;Takaaki Nishida
• 通讯作者: Takaaki Nishida

On a singular limit in Hopf bifurcation for doubly diffusive convection equations

双扩散对流方程Hopf分岔的奇异极限

• 发表时间: 2021
• 作者: Nasu Joji;Motome Yukitoshi;水田 健輔;Takuro Ideguchi;小林亜紀子,_北澤 正樹,_高橋聡,_吉川厚.;Yoshiyuki Kagei
• 通讯作者: Yoshiyuki Kagei

Hopf bifurcation in the artificial compressible system for doubly diffusive convection

双扩散对流人工可压缩系统中的 Hopf 分岔

• 发表时间: 2020
• 作者: 大窪健児;金子邦彦;Yoshiyuki Kagei
• 通讯作者: Yoshiyuki Kagei

Decay property for system of magnetohydrodynamics with Hall effect

霍尔效应磁流体动力学系统的衰变特性

• 发表时间: 2020
• 作者: 乾 幸地;求 幸年;川島秀一
• 通讯作者: 川島秀一