Local and Semi-Global Solvability for Systems of Non-Principal Type
Titel:
Local and Semi-Global Solvability for Systems of Non-Principal Type
Auteur:
Spagnolo, Sergio
Verschenen in:
Communications in partial differential equations
Paginering:
Jaargang 25 (2000) nr. 5-6 pagina's 1115-1141
Jaar:
2000
Inhoud:
We consider the N X N system[image omitted] where A(t,ξ)is a matrix valued,homogeneous symbol of order 1,and B(t,ξ) a symbol of order≤0.Denoting byµ the maximum multiplicity of the eigevalues {tj(t,ξ)} of A?(t,ξ),and assuming some regularity of these,we prove that the system is locally solvable in the Gevrey class γs,for 1≤8$le;µ/(µ-1),as soon as,for each ξ,the imaginary parts of the Tj(t,ξ)'s do not change sign for varying t and j.For 1<8<N/(N-1) the system is semi-globally solvable in γs,in particular for all f(t,x)analytic on Rn+1,and all U⊂⊂Rn+1,there is a C∞solution u(t,x) on U.
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