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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Let Lu O be a linear equation or system of equations with constant coefficients , for which the ... ( Time - like Cauchy problem for the wave equation ) .
5 Hyperbolic Equations in Higher Dimensions * 1. The Wave Equation in n - Dimensional Spacet ( a ) The method of spherical means The wave equation for a ...
( 1.31 ) ( Hint : “ Descend ” to ( 1.27 ) from the two - dimensional wave equation satisfied by u ( x1 , x2 , t ) = cos ( 4x2 ) w ( x1,1 ) .
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