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非线性分析、微分方程与动力系统系列报告

本期组织：李善兵、吴事良

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基金资助：国家自然科学基金、陕西省杰出青年科学基金

联系人：李善兵 手机：18700410622 E-mail: lishanbing@xidian.edu.cn

报告信息

(以姓氏拼音为序) 

Effects of dispersal strategies and heterogeneous environment

on total population

李 芳  中山大学

摘要：In this talk, we consider a single species model with nonlocal dispersal strategy and investigate how the dispersal rate of the species and the distribution of resources affect the total population. First, we show that the upper bound for the ratio between total population and total resource is $C\sqrt{d}$. More importantly, we provide an optimal condition on the distribution of resources such that the above ratio is of order $\squr{d}$. Secondly, for a type of simplified nonlocal diffusion operator, we prove that under certain condition, the total population as a function of dispersal rate admits exactly one local maximum point. These results reveal essential discrepancies between local and nonlocal dispersal strategies. This is joint work with Xueli Bai.

报告人简介：李芳，博士毕业于美国明尼苏达大学，现任中山大学副教授。主要研究非线性椭圆及抛物型方程（组），侧重解的定性分析。研究成果多次发表在J. Funct. Anal., J. Math. Pures Appl., Indiana Univ. Math. J., Calc. Var. Partial Differential Equations等国际数学期刊上。现主持国家自然科学基金面上项目及广东省自然科学基金面上项目。