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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This suggests , in the hyperbolic case , that one can simplify the differential equation by introducing the characteristics as new coordinate lines .
( 2.140 ) We call the differential equation or system of equations ( 2.14a ) hyperbolic ( with respect to the plane t = 0 ) , if the initial - value problem ...
We call P strictly hyperbolic when its principal part Pm ( $ , 1 ) = 0 has real distinct roots for $ # 0 hyperbolic . We see that strict hyperbolicity ...
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