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

Inhaltsangabe

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.

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