Propagation of Multidimensional Nonlinear Waves and Kinematical Conservation Laws [electronic resource] /
Prasad, Phoolan.author.
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1-4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.
Introduction -- Single first-order PDE -- Single conservation law -- Systems of hyperbolic PDE and conservation laws -- Propagation of nonlinear wave and shock -- Kinematical conservation laws (KCL) -- Conservation forms of energy transport equations -- 2-D KCL, WNLRT and SRT -- 2-D WNLRT and SRT - some applications -- 3-D WNLRT and SRT: Theory and Applications -- Appendix and Notations.
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1-4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved shock front and formation, propagation and interaction of kink lines on it.
Partial differential equations.
Computer science-Mathematics.
Computer mathematics.
Differential equations.
Partial Differential Equations.
Mathematical Applications in Computer Science.
Ordinary Differential Equations.