Uniformly symmetrizable 3×3 matrices

AbstractThe uniform symmetrizability for square matrices depending on a parameter is naturally related to the wellposedness of the Cauchy Problem for hyperbolic systems. In particular, if A(t) is a matrix function analytic in t, it is known that the Problemut=A(t)ux+B(t,x)u,u(0,x)=u0(x),is well-posed as soon as {A(t)} is US. In view of this or similar results, it is natural to look for necessary and/or sufficient conditions for the uniform symmetrizability of a family of matrices. In this paper, we give an explicit characterization of the US matrices of order ⩽3