Problems Solved and Unsolved Concerning Linear and Nonlinear Partial Differential Equations (Classic Reprint) - Softcover

Boothby, Guy Newell

Softcover

ISBN 10: 1334018014 ISBN 13: 9781334018015

Publisher: Forgotten Books, 2018

Synopsis

A concise survey of major advances in linear and nonlinear partial differential equations, with practical hints for future work and applications.

This edition introduces broad topics in PDE theory, then surveys two focused areas: linear problems and nonlinear problems. It highlights how modern tools—such as microlocal analysis, trace formulas, and spectral theory—have reshaped our understanding of wave propagation, diffraction, and the behavior of complex systems. The discussion ranges from geometric settings on manifolds to concrete problems in fluid dynamics and conservation laws, offering a snapshot of how ideas from analysis, geometry, and computation come together in PDE research.

- Learn how linear PDEs on manifolds with boundaries have seen significant progress, including wave propagation, diffractive phenomena, and spectral questions.
- See how nonlinear PDEs are approached, from viscous incompressible flows to hyperbolic conservation laws and completely integrable systems.
- Discover the interplay between energy methods, weak solutions, and modern techniques like numerical experimentation and translation representations.
- Get a sense of how non-Euclidean geometry and spectral theory influence PDE behavior, including the Laplace-Beltrami operator on negatively curved spaces.

Ideal for readers of advanced mathematics and mathematical physics who want a clear, broad view of current challenges and methods in PDE research.

About this title

About the Author

Peter D. Lax, PhD, is Professor Emeritus of Mathematics at the Courant Institute of Mathematical Sciences at New York University. Dr. Lax is the recipient of the Abel Prize for 2005 "for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions." * A student and then colleague of Richard Courant, Fritz John, and K. O. Friedrichs, he is considered one of the world's leading mathematicians. He has had a long and distinguished career in pure and applied mathematics, and with over fifty years of experience in the field, he has made significant contributions to various areas of research, including integratable systems, fluid dynamics, and solitonic physics, as well as mathematical and scientific computing.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 1334018014
• ISBN 13: 9781334018015
• Binding: Paperback
• Number of pages: 39