The singular perturbation problem for a diffusion-advection equation

扩散平流方程的奇异摄动问题

• 批准号: 09640216
• 负责人: NAKAGAWA Kiyokazu
• 金额: $ 1.66万
• 依托单位: Tohoku Gakuin University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640216/
• 关键词: diffusion-advection equation; singular perturbation; semilinear parabolic equation; behavior of solution; 拡散・移流方程式

The aim of this research project is to investigate the behavior of the solution of a diffusion-advection equation with the aid of the numerical analysis or the functional analysis. We considered at first the outline of the behavior through the numerical method. We had the numerical aspect under the useful suggestion of Professor Kawni (Chitose Science and technology University). Namely, there exists the wake after an obstacle and this was conjectured by the method of the investigation of an integral equation. This fact is not yet proved mathematically and it should be done. Each investigator considered his subject and made useful contribution.On the other hand, we investigated the behavior of the solution of the semilinear parabolic equation which is general case of a diffusion-advection equation. And we had several results. For example, we have the relation between the impulsive condition which describes the discontinuous phenomena and the stebility of the solution of the semilinear parabolic equation. And we see that the suitable impulsive condition makes a blowing-up solution stable and blows-up the solution at a desired time. We should investigate an original problem with the aid of these results.

本研究计画的目的是借由数值分析或泛函分析来探讨扩散-平流方程解的性质。我们首先通过数值方法考虑了行为的轮廓。我们在Kawni教授（甲壳糖科学技术大学）的有益建议下进行了数值方面的研究。即障碍物后存在尾流，这是用积分方程研究的方法证明的。这个事实还没有数学证明，应该这样做。另一方面，我们研究了扩散-对流方程的一般情形--半线性抛物方程解的性态。我们得到了几个结果。例如，我们给出了描述半线性抛物型方程解的不连续性的脉冲条件与解的稳定性之间的关系。我们看到，适当的脉冲条件使爆破解稳定，并在所需的时间爆破。我们应该借助这些结果来研究一个原始问题。

项目成果

Takashi Kaminogo: "Topological degree of solution mappings in functional and ordinary differntial equations" Tohoku Mathematical Journal. 49. 529-535 (1997)

Takashi Kaminogo：“泛函和常微分方程解映射的拓扑度”东北数学杂志。

Kiyokazu Nakagawa: "Asymptotic Behaviour of Solutions of an Impulsive Semilinear Parabolic Candy Problem" Proc 8^<th> Inter.Cell.on Piff Egs VSP.,Necherlands. 335-340 (1998)

Kiyokazu Nakakawa：“脉冲半线性抛物线糖果问题解的渐近行为”Proc 8^<th> Inter.Cell.on Piff Egs VSP.，Necherlands。

Kiyokazu Nakagawa: "Asymptotic behavior of solutions of an impulsive Semilinear parabolic Cauchy problem" Proceedings of the eighth international colloquium on differential equations, VSP,Netherlands. 335-340 (1998)

Kiyokazu Nakakawa：“脉冲半线性抛物线柯西问题解的渐近行为”第八届国际微分方程学术研讨会论文集，VSP，荷兰。

Takeshi Sekiguchi: "Multifractal Spectrum of Multinomial Measures" Proceedings of the Japan Academy. 73ser.A(7). 123-125 (1997)

Takeshi Sekiguchi：“多项测度的多重分形谱”日本科学院院刊。

Takeshi Sekiguchi et al.: "Multifractal Spectrum of Multinomial Measures" Proceedings of the Japan Academy. Vol.73 SerA.no.7. 123-125 (1997)

Takeshi Sekiguchi 等人：“多项测度的多重分形谱”日本科学院院刊。