Partial Differential Equations
Springer, 1982 - 249 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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A Quasi - linear System and Simple Waves Problem 46 52 53 Chapter 3 Characteristic Manifolds and the Cauchy Problem 54 1. Notation of Laurent Schwartz 54 Problems 55 2. The Cauchy Problem 56 Problems 61 3. Real Analytic Functions and ...
The Cauchy Problem for the Quasi - linear Equation We now have a simple description for the general solution u of ( 4.2 ) : The integral surface z = u ( x , y ) is the union of characteristic curves . To get a better insight into the ...
Hence the formal power series based on those Dou ; ( 0 ) actually converges and represents a solution of our Cauchy problem in a neighborhood of the origin . It remains to produce a majorising system whose solution is real analytic at 0 ...
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