Linear Partial Differential Equations And Fourier Theory
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Linear Partial Differential Equations and Fourier Theory
Author: Marcus Pivato
language: en
Publisher: Cambridge University Press
Release Date: 2010-01-07
This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.
Fourier Analysis and Nonlinear Partial Differential Equations
Author: Hajer Bahouri
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-01-03
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Lectures on Linear Partial Differential Equations
Author: Grigoriĭ Ilʹich Eskin
language: en
Publisher: American Mathematical Soc.
Release Date: 2011
This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on elementary distribution theory and Sobolev spaces. The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory.