Physics and partial differential equations. Volume I. Translated from the Chinese by Yachun Li
The book under review is concerned with the process of establishing the important fundamental partial differential equations in modern physics and a description of the mathematical structures and features of the equations. It aims at building a bridge between physics and partial differential equations, such that readers who are unfamiliar with the related physical and engineering mechanical disciplines can easily gain access to the core of the disciplines, and understand the related physical background of the partial differential equations in a short time; while readers, who are familiar with the related physical and engineering mechanical disciplines, can see the advantages of effective mathematical tools and use consequently modern mathematical concepts, methods and tools more consciously to solve related physical and engineering problems.NEWLINENEWLINEThis book is divided into two volumes, and each volume consists of five chapters. In the first five chapters (Volume I) the equations in electrodynamics, fluid dynamics, magnetohydrodynamics, reacting fluid dynamics, and elastic mechanics are considered, respectively. In each chapter, the corresponding partial differential equations are analyzed from four angles. First, the related physical and mechanical background is elaborated in a simple but profound way. Second, the whole process of establishing the equations is presented in details. Third, the mathematical structures and features are described clearly. Finally, some recent mathematical results of the related equations are introduced, including those of the authors and their research groups. Through the book, one will discover not only the connection between the physical and mechanical disciplines and their related mathematical models, but also commonly used mathematical models and their mathematical structures and features more easily.NEWLINENEWLINEThe book is very well organized and well written. It has achieved its aim mentioned above and will benefit both mathematicians, and physicists and engineers. The book is an excellent textbook for upper-level undergraduate and graduate courses. There is no doubt that this book should also be on the desk of researchers in mathematics, physics and engineering mechanics
scientific article; zbMATH DE number 6054928