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数学中最经典的模型之一。自1970年以来，人们从偏微分方程的角度对这类方程进行了深入的研究，包括一般的适定性结果和其他生物激发的解的行为（如有限时间爆破、定态解的稳定性和不稳定性、行波解、周期解等）。在过去的几十年里，人们从各种生物现象的建模中引入了越来越多的具有不同类型非局部反应的方程。该方案对具有Fisher-KPP型非局部非线性反应项的反应扩散方程（单方程和2 × 2方程组）有新的结果.对于非局部反应中含有总质量的方程，总质量的动力学性质起着重要的作用。所提出的研究包括初边值问题解的整体存在性、有限时间爆破的可能性、定态解的存在性及其稳定性分析。 并行的结果，其中涉及到一般的积分算子的非局部项追求。此外，扩散驱动的不稳定性系统将进一步讨论。这一工作将丰富非局部反应扩散方程的理论。

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

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

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

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