Quasilinear Hyperbolic Systems, Compressible Flows, and Waves

ISBN-13: 9780367384159 / Angielski / Miękka / 2019 / 282 str.

Vishnu D. Sharma

Opis

Filled with practical examples, this book 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. The author elucidates all necessary mathematical concepts in the first three chapters, including an introduction to general wave propagation problems. He highlights the application of various approaches, such as singular surface theory, asymptotic methods, and self-similarity, to solve practical physical problems from areas, including gasdynamics, radiation gasdynamics, magnetogasdynamics, nonequilibrium flows, and shallow water theory.

Spis treści

Hyperbolic Systems of Conservation Laws. Scalar Hyperbolic Equations in One Dimension. Hyperbolic Systems in One Space Dimension. Evolution of Weak Waves in Hyperbolic Systems. Asymptotic Waves for Quasilinear Systems. Self-Similar Solutions Involving Discontinuities and Their Interaction. Kinematics of a Shock of Arbitrary Strength. Bibliography. Index.

O autorze

Vishnu D. Sharma is chair professor in the Department of Mathematics at the Indian Institute of Technology, Bombay (IITB). Dr. Sharma is also president of the Indian Society of Theoretical and Applied Mechanics.