Local and Semi-Global Solvability for Systems of Non-Principal Type
Sergio Spagnolo · Communications in Partial Differential Equations · 2000
We consider the N X N system 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