Mathematics

# Approximation Theory by R. Schaback, K. Scherer PDF

By R. Schaback, K. Scherer

ISBN-10: 3540080015

ISBN-13: 9783540080015

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Sample text

Then we obtain two equations (a,+ B\$ * V ) 2 \$ - - f'"d\$- (f'1 +f (2') IV\$I'IP"l~ =o and (a,+ V\$* V \$ -f(1Y\$)4 =g It is clear that we can attain the conclusion independent of g if we find a solution of this system under a n initial condition satisfying on a n initial surface . + a =(a,+V\$ V)\$h A\$ =0 because these equations mean and + + (8, V\$ * V ) 6 Vz\$ * 6- F ( f (')(\$)u)=0 , and because the uniqueness of this linear system is also assured. The independence of g follows the uniqueness and the fact that, if \$h and \$ are sohtions for g=O, then \$ and \$+/I for g=(d/dt)%.

3) Q={(x,, x ) : --E

16] --, Applications of Nash-Moser theory to nonlinear Cauchy problems, to appear in Proc. Sym. , 45 (1986). [17] -, The Cauchy problem for hyperbolic equations with double characteristics, Publ. , 19 (1983), 927-942. [18] K. Kajitani, Cauchy problem for non-strictly hyperbolic systems, Publ. , 15 (1979), 519-550. [19] K. Kasahara and M. Yamaguti, Strongly hyperbolic system of linear partial differential equations with constant coefficients, Mem. COIL Sci. , Ser A, 33 (1960), 1-23. [20] A. Lax, On Cauchy’s problem for partial differential equations with mulitiple characteristics, Comm.