Daniel D. Joseph Bücher

Focusing on the elasticity of liquids, this book explores the mathematical and physical implications within rheological fluid mechanics. It discusses how instantaneously elastic constitutive models can create hyperbolic dynamics, leading to phenomena like shear waves and shock waves. The text also examines how certain models with low viscosities result in perturbed elasticity, smoothing discontinuities akin to gas dynamics. Additionally, it highlights the rapid response of liquids to impulses and contrasts this with their eventual viscous behavior, emphasizing relaxation times and implications for engineering applications.

This substantially revised second edition teaches the bifurcation of asymptotic solutions to evolution problems governed by nonlinear differential equations. Written not just for mathematicians, it appeals to the widest audience of learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at foundation level, while the applications and examples are specially chosen to be as varied as possible.