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Research on global solutions in time and their asymptotic behaviors for viscous and relaxation models of conservation laws

守恒定律粘性和松弛模型的时间全局解及其渐近行为研究

基本信息

批准号：
15340043
负责人：
MATSUMURA Akitaka
金额：
$ 10.3万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2006
项目状态：
已结题

项目摘要

1.Initial boundary value problems on the half space to one-dimensional isentropic models for compressible fluid are investigated. In a case where the fluid inflows on the boundary, it is proved that the superposition of the boundary layer solution and viscous shock wave (or rarefaction wave) is asymptotically stable under some smallness conditions. In a case where the fluid outflows on the boundary, the existence of the boundary layer solution and its asymptotic stability are also proved. Furthermore, an initial boundary value problem on the half space to a one-dimensional ideal gas model (3 by 3 system) is investigated, and then the asymptotic stability of the viscous contact wave is proved. The asymptotic stability of the viscous contact wave for the Cauchy problem is also proved, if the integral of the initial perturbation is zero. Among multi-dimensional problems, it is proved that the spherically symmetric solution of an isothermal model of the compressible Navier-Stokes equation … More globally exists in time and tends toward its stationary solution.2.Initial boundary value problems for a one-dimensional model which describes the movement of electrons in semiconductors are investigated. It is proved that even for any large doping profile the stationary solution exits and is asymptotically stable. As for the multi-dimensional models, an iterative algorithm of numerical computation with high resolution to simulate the stationary solutions is developed.3.Asymptotic behavior of solutions of a one-dimensional model of compressible viscous fluid in porous media is investigated. It is proved that the solution tends toward a diffusion wave of a parabolic equation, and the precise decay rate of asymptotics to the diffusion wave is also obtained.4.Asymptotic behavior of solutions of nonlinear dispersive equations and dissipative equations with a critical nonlinearity is investigated. It is proved that the solution of dissipative wave equation tends toward a self-similar solution of a heat equation. As for the dispersive equations, a new result on how the resonance phenomena between the characteristic frequency number of the linearized equation and that of nonlinear term influences the asymptotic behavior of the solutions. Less

1.研究了一维可压缩流体等熵模型在半空间上的初边值问题。在边界上有流体流入的情况下，证明了边界层解与粘性激波(或稀疏波)的叠加在一定的小条件下是渐近稳定的。在流体在边界上流出的情况下，证明了边界层解的存在性及其渐近稳定性。在此基础上，研究了一维理想气体模型(3×3系统)在半空间上的初边值问题，证明了粘性接触波的渐近稳定性。当初始摄动积分为零时，证明了柯西问题粘性接触波的渐近稳定性。在多维问题中，证明了可压缩N-S方程的等温模型…的球对称解在时间上更具全局性，并且趋于其定常解。2.研究了描述电子在半导体中运动的一维模型的初边值问题。证明了即使对于任何大的掺杂分布，稳态解也存在并且是渐近稳定的。对于多维模型，提出了一种高分辨率的数值计算迭代算法来模拟定常解。3.研究了多孔介质中一维可压缩粘性流体模型解的渐近行为。证明了解趋向于抛物方程的扩散波，并得到了渐近于扩散波的精确衰减率。4.研究了具有临界非线性的非线性色散方程和耗散方程解的渐近行为。证明了耗散波动方程的解趋于热方程的自相似解。对于色散方程，得到了线性化方程的特征频率数与非线性项的特征频率数之间的共振现象对解的渐近行为的影响的一个新结果。较少

项目成果

期刊论文数量（37）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

S.Doi: "Singularities of solutions of Schroedinger equations for perturbed harmonic oscillators""Hyperbolic Problems and RelatedTopics," Internatinal Press, Somerville, MA. 185-199 (2003)

S.Doi：“扰动谐振子薛定谔方程解的奇异性”“双曲问题和相关主题”，国际出版社，萨默维尔，马萨诸塞州。

DOI：
发表时间：
期刊：
影响因子：
0
作者：
通讯作者：

Multidimensional discretization of the quantum drift-diffusion model for ultrasmall MOSFET structures

超小型 MOSFET 结构量子漂移扩散模型的多维离散化

DOI：
发表时间：
2004
期刊：
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 23
影响因子：
0
作者：
K.Nishihara;T.Yang;H.Zhao;S.Odanaka
通讯作者：
S.Odanaka

Viscous shock wave to a gas-solid free boundary problem for compressible viscous gas

粘性激波对可压缩粘性气体气固自由边界问题的影响