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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Along a noncharacteristic curve the Cauchy data uniquely determine the second derivatives of u on y . As a matter of fact , we can then also find ...
We are to find a solution u near S which has these Cauchy data on S. We call S noncharacteristic if we can get all D'u for sal = m on S from the linear ...
But the restriction to analytic Cauchy data and solutions is unrealistic . It implies that the solution is determined globally by local conditions near one ...
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