Dynamics of solutions near space-periodic bifurcating steady solutions of thermal convection equations

热对流方程空间周期分岔稳态解附近解的动力学

基本信息

批准号：
11640208
负责人：
KAGEI Yoshiyuki
金额：
$ 2.43万
依托单位：
KYUSHU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640208/
关键词：
Oberbeck-Boussinesq equation Bifurcation Asympotic behavior 解の安定性解の慚正挙動

项目摘要

Y.Kagei showed that some stationary solutions of the Obebeck-Boussinesq equation is unconditionally stable even when they are at criticality of the linearized stability. Kagei then derived a model equation of thermal convection in which the effect of viscous dissipative heating is taken into account. It was shown that the threshold of the onest of convection for this model equation is larger than that for the usual Oberbeck-Boussinesq equation and various space-periodic stationary solutions bifurcate at the threshold transcritically. Kagei also studied the Cauchy problem for the Vlasov-Poisson-Fokker-Planck equation and constructed invariant manifolds in some weighted Sobolev spaces. As a result, long-time asymptotics of small solutions were derived. S.Kawashima studied a singular limit problem for a general hyperbolic-elliptic system and proved that in the singular limit the solution of the hyperbolic-elliptic system converges to the solution of the corresponding hyperbolic-parabolic system. Kawashima also studied initial boundary value problems for discrete Boltzmann equations in the half-space and showed the existence of stationary solutions under several boundary conditions and their asymptotic stability. T.Ogawa showed that for a class of semilinear dispersive equations, solutions with initial values having one singular point like the Dirac delta function become real analytic in space and time variables except at the initial time. Ogawa also studied blow-up problem for the three dimensional Euler equation and gave a sufficient condition for blow-up in terms of some semi-norm of a generalized Besov space. T.Iguchi studied bifurcation problem of stationary surface waves and classified possible bifurcation patterns.

Y.Kagei表明，即使在线性化稳定性的急切性时，Obebeck-Boussinesq方程的某些固定溶液也无条件稳定。然后，Kagei得出了热对流的模型方程，其中考虑了粘性耗散加热的影响。结果表明，该模型方程的对流的阈值大于通常的Oberbeck-Boussinesq方程和各种空间周期性固定溶液在经过限制的阈值处分叉的阈值。 Kagei还研究了Vlasov-Poisson-Fokker-Planck方程的Cauchy问题，并在某些加权的Sobolev空间中构建了不变的歧管。结果，得出了小溶液的长期渐近学。 S.Kawashima研究了一般双曲线 - 纤维化系统的单一极限问题，并证明在单数极限中，双曲线 - 纤维化系统的解决方案会收敛到相应的双曲线 - 促支持者系统的溶液。川岛还研究了半空间中离散玻尔兹曼方程的初始边界值问题，并在几个边界条件及其渐近稳定性下显示了固定溶液的存在。 T.Ogawa表明，对于一类半连续分散方程，具有一个单个点的奇数点（如Dirac Delta函数）在时空和时段变量中具有真实分析，除了初始时间以外。 Ogawa还研究了三维Euler方程的爆炸问题，并提供了足够的条件，可以在某些半符号的广义BESOV空间中进行爆炸。 T.iguchi研究了固定表面波和分类的分叉模式的分叉问题。