Singularities: Formation, Structure, and Propagation

Many natural phenomena are described as singularities, for example, the formation of drops and bubbles, or the motion of cracks. Aimed at a broad audience of students and researchers in mathematics, physics and engineering, this book provides mathematical tools for understanding all aspects of singularities.

Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.