On a study on dynamics of localized pattern for a bistable reaction diffusion equations with a heterogeneous environment

异质环境下双稳态反应扩散方程局域模式动力学研究

• 批准号: 23740137
• 负责人: HIROSHI Matsuzawa
• 金额: $ 1.08万
• 依托单位: Numazu National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23740137/
• 关键词: 反応拡散方程式; 自由境界問題; 偏微分方程式; 放物型方程式; spreading speed; 双安定; 遷移層; 進行波

In this research, we study free boundary problems for nonlinear diffusions equations. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundaries representing the expanding fronts. If the nonlinearity is monostable, bistable, or combustion type, Professor Du and Professor Lou obtained a rather complete description of the long-time dynamical behavior of the problem and revealed sharp transition phenomena between so called "spreading" and "vanishing". They also determined the asymptotic spreading speed of the fronts by using of "semi-waves" when spreading happens. In this research we we give a much sharper estimate for the spreading speed of the fronts than that in the work of Du and Lou, and we describe how the solution approaches the semi-wave when spreading happens. I obtained these results for (1)1 dimensional problem, (2)higher dimensional problem with radially symmetric setting and (3)1 dimensional advection-diffusion problem.

本文研究了非线性扩散方程的自由边界问题。这样的问题可以用来描述生物或化学物种的扩散，自由边界代表扩张的前沿。如果非线性是单稳态、双稳态或燃烧型，杜教授和娄教授对问题的长期动力学行为得到了相当完整的描述，并揭示了所谓的“扩散”和“消失”之间的急剧过渡现象。他们还利用“半波”确定了扩散发生时锋面的渐近扩散速度。在本研究中，我们对锋面的扩散速度给出了比Du和Lou的工作更精确的估计，并描述了在扩散发生时解是如何接近半波的。我在(1)一维问题，(2)具有径向对称设置的高维问题和(3)一维平流扩散问题中得到了这些结果。

项目成果

Spreading speed and asymptotic profiles for solutions in free boundary problems for nonlinear

非线性自由边界问题解的扩展速度和渐近轮廓

• 发表时间: 2014
• 作者: Yihong Du;Hiroshi Matsuzawa and Maolin Zhou;Hiroshi Matsuzawa
• 通讯作者: Hiroshi Matsuzawa

Spreading speed and profile for nonlinear Stefan problems in high space dimensions

• DOI: 10.1016/j.matpur.2014.07.008
• 发表时间: 2015-03
• 期刊: Journal de Mathématiques Pures et Appliquées
• 作者: Yihong Du;H. Matsuzawa;Maolin Zhou

Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems

• DOI: 10.1137/130908063
• 发表时间: 2014-01
• 期刊: SIAM J. Math. Anal.
• 作者: Yihong Du;H. Matsuzawa;Maolin Zhou

Spreading speed and profile for nonlinear diffusion problems with free boundaries

具有自由边界的非线性扩散问题的传播速度和轮廓

• 发表时间: 2013
• 作者: Y. Sakata;T. Minezaki et al.;Hiroshi Matsuzawa
• 通讯作者: Hiroshi Matsuzawa

Spreading speed and asymptotic profiles for solutions in free boundary problems for nonlinear advection-diffusion equations

非线性平流扩散方程自由边界问题解的传播速度和渐近剖面

• 作者: 諸隈智貴;冨永望;田中雅臣;Tomoki Morokuma;Hiroshi Matsuzawa
• 通讯作者: Hiroshi Matsuzawa