Filled with practical examples, Quasilinear Hyperbolic Systems,
Compressible Flows, and Waves presents a self-contained discussion
of quasilinear hyperbolic equations and systems with applications.
It emphasizes nonlinear theory and introduces some of the most
active research in the field. After linking continuum mechanics and
quasilinear partial differential equations, the book discusses the
scalar conservation laws and hyperbolic systems in two independent
variables. Using the method of characteristics and singular surface
theory, the author then presents the evolutionary behavior of weak
and mild discontinuities in a quasilinear hyperbolic system. He
also explains how to apply weakly nonlinear geometrical optics in
nonequilibrium and stratified gas flows and demonstrates the power,
generality, and elegance of group theoretic methods for solving
Euler equations of gasdynamics involving shocks. The final chapter
deals with the kinematics of a shock of arbitrary strength in three
dimensions. With a focus on physical applications, this text takes
readers on a journey through this fascinating area of applied
mathematics. It provides the essential mathematical concepts and
techniques to understand the phenomena from a theoretical
standpoint and to solve a variety of physical problems.
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