Nonlinear Hyperbolic Waves in Multidimensions (Google eBook)
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.
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amplitude approximate assume caustic characteristic conoid characteristic curves characteristic field characteristic surface coefficients compatibility conditions conservation laws consider constant denote discontinuity domain eigenvalue eikonal equation entropy equa Euler's equations expression Fermat's principle finite function gas dynamics genuine nonlinearity geometrical given Hence Huygens hyperbolic system independent variables infinite system initial condition initial data initial shock front initial value problem initial wavefront jump kinks linear rays linear wavefront neighbourhood nonlinear wave nonlinear wavefront numerical obtained parameter partial differential equation perturbation piston plane polytropic gas pulse quantity ray equations represents Riemann invariants right hand side satisfies shock dynamics shock front shock ray theory shock strength singular point sonic point steady solution successive positions system of equations tangential derivatives theorem theory of shock tion transonic transport equation unit normal valid vector wave equation wavefront Qt weak shock weak solution weakly nonlinear Whitham's WNLRT x-axis y)-plane
Page ii - Berlin P. Bullen, University of British Columbia RJ Elliott, University of Alberta RP Gilbert, University of Delaware R. Glowinski, University of Houston D. Jerison, Massachusetts Institute of Technology K. Kirchgassner, Universitat Stuttgart B. Lawson, State University of New York B. Moodie, University of Alberta LE Payne, Cornell University DB Pearson, University of Hull GF Roach, University of Strathclyde I.