Tai-Ping Liu – författare

This book presents the fundamentals of the shock wave theory. The first part of the book, Chapters 1 through 5, covers the basic elements of the shock wave theory by analyzing the scalar conservation laws.The main focus of the analysis is on the explicit solution behavior. This first part of the book requires only a course in multi-variable calculus, and can be used as a text for an undergraduate topics course. In the second part of the book, Chapters 6 through 9, this general theory is used to study systems of hyperbolic conservation laws. This is a most significant well-posedness theory for weak solutions of quasilinear evolutionary partial differential equations. The final part of the book, Chapters 10 through 14, returns to the original subject of the shock wave theory by focusing on specific physical models. Potentially interesting questions and research directions are also raised in these chapters.The book can serve as an introductory text for advanced undergraduate students and for graduate students in mathematics, engineering, and physical sciences. Each chapter ends with suggestions for further reading and exercises for students.

This volume presents seven invited lecture series from the DFG Priority Programme Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness, surveying recent developments in mathematical fluid dynamics across a broad range of scales, from kinetic theory to turbulence, mixing, and relativistic flows. The contributions reflect current research directions in the field. Hana Mizerová and Simon Markfelder discuss aspects of the emerging theory of non-standard weak and generalized solutions to the compressible Euler equations. Theodore Drivas addresses turbulence, Gianluca Crippa studies mixing phenomena, Tai‑Ping Liu and Shih‑Hsien Yu develop the theory of nonlinear waves for the Boltzmann equation, and Marcelo Disconzi focuses on dissipative relativistic fluid dynamics.The volume is intended for researchers and advanced graduate students in partial differential equations and applied mathematics.

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.