Remarks on the Mathematical Theory of Detonation and Deflagration Waves in Gases: Supplement to the Manual on Supersonic Flow and Shock Waves

by Richard Courant

This book delves into the mathematical theory of detonation and combustion waves in gases. The author, a renowned mathematician, explores the complex phenomena that occur when reactions involving detonation or combustion take place in gases, providing a systematic analysis of the mathematical possibilities of such flows with one-dimensional motion. The author begins by presenting the basic concepts and assumptions underlying the theory, including the laws of conservation, and the transition conditions across reaction fronts. The text then examines the determinacy of reaction waves, analyzing the interplay between the characteristics of the system of differential equations and the reaction front. This analysis leads to the identification of two key detonations and deflagrations, with the Chapman-Jouguet rule playing a crucial role in determining the properties of these reactions. The book goes on to explore the various possibilities for flows involving reaction fronts, considering both supersonic and subsonic flows, as well as weak and strong detonations and deflagrations. The author demonstrates how the adjustment of the flow to the boundary conditions depends on the type of reaction and the initial conditions. This book offers a comprehensive treatment of the mathematical theory of detonation and combustion waves in gases, providing valuable insights into the fundamental principles governing these phenomena. Its rigorous mathematical approach and detailed analysis make it an essential resource for researchers and graduate students in applied mathematics, fluid dynamics, and combustion theory.

57 pages, Hardcover

Published August 24, 2018

About the author

Richard Courant (January 8, 1888 – January 27, 1972) was a German American mathematician. He is best known by the general public for the book What is Mathematics?, co-written with Herbert Robbins.