Nonlinear wave equations
Author(s)
Bibliographic Information
Nonlinear wave equations
（Regional conference series in mathematics, no. 73）
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c1989
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Note
"Expository lectures from the CBMS Regional Conference, held at George Mason University January 16-20, 1989"--T.p. verso
"Supported by the National Science Foundation."
Bibliography: p. 87-91
Description and Table of Contents
Description
The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area.The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
Table of Contents
Invariance Existence Singularities Solutions of small amplitude Scattering Stability of solitary waves Yang-Mills equations Vlasov-Maxwell equations.
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