Nonlinear Hyperbolic Waves in Multidimensions (PDF)

The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts in gas dynamics, a graphical presentation of the results of extensive numerical computations, and an extension of Fermat's principle. There is also a chapter containing approximate equations used to discuss stability of steady transonic flows.Full of new and original results, Nonlinear Hyperbolic Waves in Multidimensions is your only opportunity to explore a full treatment of these recent findings in book form. The material presented in this volume will prove useful not only for solving practical problems, but also in raising many difficult but important mathematical questions that remain open.