Analysis on Fisher-KPP type nonlocal reaction diffusion equations

Fisher-KPP型非局部反应扩散方程分析

• 批准号: 290265139
• 负责人: Professorin Li Chen, Ph.D.
• 金额: --
• 依托单位: Chair in Applied Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/290265139?language=en
• 关键词: Analysis; Fisher; KPP; type; nonlocal

Reaction diffusion equations are one of the most classical models in biomath. Since 1970, these equations from PDE point of view have been well studied, including the general wellposedness results and other biological motivated solution behaviors (for example, finite time blow up, stability and instability of the stationary solutions, the traveling wave solutions, periodic solutions and other patterns). In the last decades, more and more equations with different type of nonlocal reactions were introduced from the modeling of different biological phenomena. This proposal aspires new results on reaction diffusion equations (a single equation and a 2x2 system) with Fisher-KPP type nonlocal nonlinear reaction terms. For the equations with total masses in the nonlocal reactions, the dynamic of total masses plays an important role. The proposed research includes the global existence of solutions to an initial boundary value problem, the possibility of finite time blow up, the existence of stationary solutions and their stability analysis. Parallel results for the nonlocal term which involves the general integral operator are pursued. In addition, the diffusion driven instability for systems will be further discussed. This proposed project will enrich the current theories on nonlocal reaction diffusion equations.

反应扩散方程是生物模型中最古典的模型之一。自1970年以来，对PDE角度的这些方程进行了充分的研究，包括一般性良好的结果和其他生物动机的溶液行为（例如，有限的时间爆炸，固定溶液的稳定性和不稳定，波动波解决方案，周期溶液和其他模式）。在过去的几十年中，通过不同生物学现象的建模引入了越来越多的具有不同类型的非局部反应的方程式。该提案允许使用Fisher-KPP型非局部非线性反应项的反应扩散方程（单个方程式和2x2系统）的新结果。对于非局部反应中总质量的方程式，总质量的动态起着重要作用。拟议的研究包括针对初始边界价值问题的全球解决方案，有限时间爆炸的可能性，固定解决方案的存在及其稳定性分析。 追求涉及一般积分运算符的非本地术语的并行结果。此外，将进一步讨论扩散驱动的系统的不稳定性。该提出的项目将在非局部反应扩散方程上丰富当前理论。

项目成果

Chemotaxis model with nonlocal nonlinear reaction in the whole space

• DOI: 10.3934/dcds.2018222
• 发表时间: 2018-07
• 作者: S. Bian;Li Chen;E. Latos

Wavefronts for a nonlinear nonlocal bistable reaction–diffusion equation in population dynamics

• DOI: 10.1016/j.jde.2017.07.019
• 发表时间: 2017-01
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: Li Chen;E. Latos;Jing Li

A nonlocal reaction diffusion equation and its relation with Fujita exponent

非局部反应扩散方程及其与Fujita指数的关系

• DOI: 10.1016/j.jmaa.2016.07.014
• 发表时间: 2015-10
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: Shen Bian;Li Chen
• 通讯作者: Li Chen

Global existence and asymptotic behavior of solutions to a nonlocal Fisher-KPP type problem

非局部 Fisher-KPP 型问题解的全局存在性和渐近行为

• DOI: 10.1016/j.na.2016.10.017
• 发表时间: 2015-08
• 期刊: Nonlinear Analysis
• 作者: Bian Shen;Chen Li;Latos Evangelos
• 通讯作者: Latos Evangelos

Nonlocal nonlinear reaction preventing blow-up in supercritical case of chemotaxis system

趋化系统超临界情况下防止爆炸的非局部非线性反应

• DOI: 10.1016/j.na.2018.06.012
• 发表时间: 2018-11
• 期刊: Nonlinear Analysis
• 作者: Shen Bian;Li Chen;Evangelos Latos
• 通讯作者: Evangelos Latos