Partial Differential Equations

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Springer Science & Business Media, 1991 M11 20 - 252 páginas

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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Chapter
1
Quasilinear Equations
9
Chapter 3
39
Chapter 8
53
Characteristic Manifolds and the Cauchy Problem
54
The Cauchy Problem
58
The LagrangeGreen Identity
79
Distribution Solutions
89
45
137
HigherOrder Hyperbolic Equations with Constant Coefficients
143
www
150
Symmetric Hyperbolic Systems
163
37
175
Chapter 6
185
More on the Hilbert Space H and the Assumption of Boundary Values
198
Chapter 7
206

The Maximum Principle
103
Proof of Existence of Solutions for the Dirichlet Problem Using
111
Solution of the Dirichlet Problem by HilbertSpace Methods
117
Chapter 5
126
The OneDimensional Wave Equation
128
The InitialValue Problem for General SecondOrder Linear
227
H Lewys Example of a Linear Equation
235
Bibliography
241
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