Nonlinear Problems Of Compressible Flow

This book presents an analytical study of fluid pressure generated by wave fronts moving over the surface of a compressible fluid. Beginning with a clear formulation of the physical and mathematical problem, it systematically develops both linear and nonlinear approaches to wave propagation. Particular attention is given to sound and shock waves, including pressure behaviour near wave fronts, sonic lines, and regions of contact. The text carefully builds from two-dimensional formulations to axisymmetric cases, emphasising the limits of approximation methods, especially the validity of the Whitham method in higher-order analyses. In the later chapters, the focus shifts to pressure distribution under arbitrary boundary conditions in a half-space, addressing complex phenomena such as shock wave motion, long-time behaviour, and transitions through the speed of sound. The comparison between linear and nonlinear formulations is extended to inhomogeneous, compressible, conducting, and viscous fluids. Detailed appendices support the main text with complementary mathematical treatments, making the book a valuable reference for advanced students and researchers interested in wave dynamics, fluid mechanics, and applied mathematics. Translated by I. Shechtman Edited by P. Greenberg