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Adaptive evolution and concentrations in parabolic PDEs
发布时间: 2018-04-23     09:19   【返回上一页】 发布人:Beniot Perthame


北京师范大学数学科学学院

 

公众报告

 

 

报告题目: Adaptive evolution and concentrations in parabolic PDEs

 

报告人:Beniot Perthame 教授(巴黎六大、法国科学院院士)

 

时间地点:2018年4月25日下午4:00-5:00 后主楼1124

 

邀请人:许孝精

 

报告摘要: Living systems are characterized by variability; in the view of C.~Darwin, they are subject to constant evolution through the three processes of population growth, selection by nutrients limitation and mutations.

     Several mathematical theories have been proposed in order to describe  the dynamics generated by the interaction between their environment and the trait selection of the `fittest'. One can use stochastic idividual based models, dynamical systems, game theory considering traits as strategies. From a populational point of view, the population obeys an integro-partial-differential equation for the density number.

     We will give a self-contained mathematical model of such dynamics and show that an asymptotic method allows us to formalize precisely the concepts of monomorphic or polymorphic population. Then, we can describe the evolution of the ‘fittest trait’ and eventually to compute various forms of branching points which represent the cohabitation of two different populations.

     The concepts are based on the asymptotic analysis of the above mentioned parabolic equations once appropriately rescaled. This leads to concentrations of the solutions and the difficulty is to evaluate the weight and position of the moving Dirac masses that describe the population. We will show that a new type of Hamilton-Jacobi equation, with constraints, naturally describes this asymptotic.

     Recent developments concern non-proliferative advantages and lead to define the notion of  'effective fitness'.

 

报告人简介:Benoit Perthame教授是Université Pierre et Marie Curie(巴黎第六大学)的最高等级教授,法国科学院院士,欧洲院士(Member of Academia Europaea)。2014年国际数学家大会(ICM)的大会特邀报告人(1小时),2013年国际工业与应用数学大会的大会特邀报告人。他在微分方程、生物数学、计算数学等众多领域做出了杰出的贡献,是当今世界最具影响力的数学家之一。

 

 

周五学院公众报告主旨:讲解现代数学中的基本概念、重要结果及其数学思想的起源、方法的创新等,扩展我们的教师和研究生的视野、提高数学修养以及增强学院的学术氛围。邀请各方向的专家用通俗易懂的报告内容、自由互动的讲解方式展现现代数学中重要的基本概念和深刻原理,让听众可以领略到现代数学理论其实是来源于一些大学或研究生阶段就熟知的古典数学中的想法和结论。希望这些报告有助于高年级的本科生、研究生和教师更全面的认识现代数学、享受数学之美。欢迎大家踊跃参与!