The Mathematics of Diffusion
The Mathematics of Diffusion
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DOI：
10.1088/0031-9112/7/10/004
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发表时间：
2011-09
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影响因子：
--
通讯作者：
W. Ni
中科院分区：
文献类型：
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作者：
W. Ni
扩散在许多科学学科中被广泛用于模拟各种各样的现象。扩散数学侧重于非线性椭圆和抛物方程和系统的解的定性性质，与域几何形状，各种边界条件，不同扩散速率的机制以及扩散和空间异质性之间的相互作用。这本书系统地探讨了不同的扩散率之间的相互作用，从模式形成的观点，特别是图灵的扩散驱动的不稳定性在均质和异质性的环境，和随机扩散的作用，定向运动，和空间异质性在经典的洛特卡-沃尔泰拉竞争系统。贯穿全书的是许多简单的，基本的，重要的开放式问题，供读者调查。读者：这本书是为研究人员和研究生在椭圆或抛物方程和数学生物学领域。目录：序言;第1章。第二章热方程（The Heat Equation）一般反应扩散方程和系统的动力学;第3章。反应扩散方程和系统稳态的定性性质;第4章。异质环境中的扩散：2 × 2 Lotka-Volterra竞争系统;第5章。超越扩散：定向运动，出租车，交叉扩散;参考书目;索引。
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical Lotka-Volterra competition systems. Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate. Audience: This book is intended for researchers and graduate students in the areas of elliptic or parabolic equations and in mathematical biology. Contents: Preface; Chapter 1. Introduction: The Heat Equation; Chapter 2. Dynamics of General Reaction-Diffusion Equations and Systems; Chapter 3. Qualitative Properties of Steady States of Reaction-Diffusion Equations and Systems; Chapter 4. Diffusion in Heterogeneous Environments: 2 x 2 Lotka-Volterra Competition Systems; Chapter 5. Beyond Diffusion: Directed Movements, Taxis, and Cross-Diffusion; Bibliography; Index.