本教材分两部分，重点介绍自相似解在研究非线性偏微分方程，尤其是抛物型偏微分方程解的行为中的作用。该论述系统地从基本概念转移到更复杂的概念，包括最近的发展和几个开放的问题。通过具有挑战性的练习、示例和插图，帮助解释Navier–Stokes方程、平均曲率流方程和其他描述真实现象的重要方程的严格分析基础，本书不仅面向数学领域的研究生和研究人员，也面向其他学科的研究生和研究人员。
非线性偏微分方程将作为现代分析第一门课程的优秀教材或有用的自学指南。介绍了非线性偏微分方程中的关键问题，以及一些基本工具和方法。唯一的先修课程是微积分基础课程。
Nonlinear Partial Differential Equations: Asymptotic Behavior of Solutions and Self-Similar Solutions
The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.
Nonlinear Partial Differential Equations will serve as an excellent textbook for a first course in modern analysis or as a useful self-study guide. Key topics in nonlinear partial differential equations as well as several fundamental tools and methods are presented. The only prerequisite required is a basic course in calculus.
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