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.
Resultados 1-3 de 55
This suggests , in the hyperbolic case , that one can simplify the differential
equation by introducing the characteristics as new coordinate lines . Let $ = $ ( x ,
y ) = const . , n = 4 ( x , y ) = const . be the two families of characteristics in the xy ...
( 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 ( 2.14a ,
b , c ) has a solution u ( x , t ) of class Co , for all g ( x ) E Cʻ ( R " ) , where s is
We call P strictly hyperbolic when its principal part Pm ( $ , 1 ) = 0 has real distinct
roots for $ # 0 hyperbolic . We see that strict hyperbolicity implies hyperbolicity .
Thus , for example , any equation of the form c ? Au + ku ( 2.44 ) is hyperbolic .
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