Partial Differential Equations

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Springer Science & Business Media, Nov 20, 1991 - Mathematics - 252 pages

This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation without solutions.

 

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standard textbook on PDE

Contents

Chapter
1
Quasilinear Equations
9
Examples
15
The Cauchy Problem
24
Chapter 2
33
The OneDimensional Wave Equation
40
Systems of FirstOrder Equations
46
A Quasilinear System and Simple Waves
52
Proof of Existence of Solutions for the Dirichlet Problem Using
111
Solution of the Dirichlet Problem by HilbertSpace Methods
117
HigherOrder Hyperbolic Equations with Constant Coefficients
143
Symmetric Hyperbolic Systems
163
Chapter 6
186
Chapter 8
192
More on the Hilbert Space g and the Assumption of Boundary Values
198
Chapter 7
206

The LagrangeGreen Identity
79
Distribution Solutions
89
The Maximum Principle
103
H Lewys Example of a Linear Equation
235
Bibliography
241
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