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| 1 | 关于肿瘤增长和治疗的一些数学知识显示文摘用偏微分方程或者自由边值问题描述肿瘤增长的数学模型现在是预测一些癌症演化的重要工具,例如基于图像分析的模型.这些模型不仅可以在医疗上预测癌症的演化,还可以用来帮助理解组织生长过程中生物的和机械的效果,以及给出最优的治疗方案,甚至在某些情况下预测失败的治疗方案. | Benoit Perthame 黄际政 孙宇阳 | 2014 | 数学译林2014，0，4： | 0 |
| 2 | Dirac Concentrations in a Chemostat Model of Adaptive Evolution(In honor of the immense scientific influence of Ham Brezis)显示文摘This paper deals with a non-local parabolic equation of Lotka-Volterra type that describes the evolution of phenotypically structured populations. Nonlinearities appear in these systems to model interactions and competition phenomena leading to selection. In this paper, the equation on the structured population is coupled with a differential equation on the nutrient concentration that changes as the total population varies.Different methods aimed at showing the convergence of the solutions to a moving Dirac mass are reviewed. Using either weak or strong regularity assumptions, the authors study the concentration of the solution. To this end, BV estimates in time on appropriate quantities are stated, and a constrained Hamilton-Jacobi equation to identify where the solutions concentrates as Dirac masses is derived. | Alexander LORZ Benoit PERTHAME Cécile TAING | 2017 | Chinese Annals of Mathematics,Series B2017，38，2： | 0 |
| 3 | Transversal Instability for the Thermodiffusive Reaction-Diffusion System显示文摘The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, and growth of bacterial colonies. Since a scalar equation generates usually stable waves, the simplest mathematical description relies on two-by-two reaction-diffusion systems. The authors' interest is the extension of the Fisher/KPP equation to a two-species reaction which represents reactant concentration and temperature when used for flame propagation,and bacterial population and nutrient concentration when used in biology.The authors study circumstances in which instabilities can occur and in particular the effect of dimension. It is observed numerically that spherical waves can be unstable depending on the coefficients. A simpler mathematical framework is to study transversal instability, which means a one-dimensional wave propagating in two space dimensions.Then, explicit analytical formulas give explicitely the range of paramaters for instability. | Michal KOWALCZYK Benoit PERTHAME Nicolas VAUCHELET | 2015 | Chinese Annals of Mathematics,Series B2015，36，5： | 0 |
| 4 | Analysis of a System Describing Proliferative-Quiescent Cell Dynamics显示文摘Systems describing the dynamics of proliferative and quiescent cells are commonly used as computational models, for instance for tumor growth and hematopoiesis.Focusing on the very earliest stages of hematopoiesis, stem cells and early progenitors, the authors introduce a new method, based on an energy/Lyapunov functional to analyze the long time behavior of solutions. Compared to existing works, the method in this paper has the advantage that it can be extended to more complex situations. The authors treat a system with space variable and diffusion, and then adapt the energy functional to models with three equations. | Jean CLAIRAMBAULT Benoit PERTHAME Andrada Quillas MARAN | 2018 | Chinese Annals of Mathematics,Series B2018，39，2： | 0 |
| 5 | Composite Waves for a Cell Population System Modeling Tumor Growth and Invasion显示文摘In the recent biomechanical theory of cancer growth,solid tumors are considered as liquid-like materials comprising elastic components.In this fluid mechanical view,the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate,with the latter depending on the local cell density(contact inhibition) or/and on the mechanical stress in the tumor.For the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modeling,the authors prove that there are always traveling waves above a minimal speed,and analyse their shapes.They appear to be complex with composite shapes and discontinuities.Several small parameters allow for analytical solutions,and in particular,the incompressible cells limit is very singular and related to the Hele-Shaw equation.These singular traveling waves are recovered numerically. | Min TANG Nicolas VAUCHELET Ibrahim CHEDDAD Irene VIGNON-CLEMENTEL Dirk DRASDO Benoit PERTHAME | 2013 | Chinese Annals of Mathematics,Series B2013，34，2： | 0 |
| 6 | 什么是退化抛物-双曲型方程的动理学解?显示文摘非线性退化抛物一双曲型方程是最重要的几类非线性偏微分方程之一.非线性与退化性是这些方程的两个主要特征,它们产生了一些异乎寻常的现象,这些现象需要用新的数学思想、方法和理论来加以解释.另一方面,由于这类方程在实际应用中的重要性,已有了有关计算此类方程的解的各种数值方法的设计与分析的大量文献.此外,此类方程解的适定性理论(存在性、唯一性和稳定性)的研究更迫在眉睫. | 陈贵强 Benoit Perthame 甘在会(译) 陆柱家(校) | 2012 | 数学译林2012，31，4： | 0 |
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