Canonical forms of \(3\times 3\) strongly and nonstrictly hyperbolic systems with complex constant coefficients
Consider a \(3 \times 3\) system of differential equations \(\partial u/ \partial t = \sum^ n_{i=1} A_ i \partial u/ \partial x_ i\), where \(u\) is a 3-vector and \(A_ i\) are complex constant \(3 \times 3\) matrix coefficients. Here the independent variables \(x_ i\) \((i=1,\dots,n)\) and \(t\) are real. In a previous paper [J. Math. Kyoto Univ. 31, No. 4, 937-982 (1991; reviewed above)], the present author classified the strongly hyperbolic \(3 \times 3\) systems with real constant coefficients. The purpose of this paper is to study the same problem for the \(3 \times 3\) systems with complex constant coefficients, limiting ourselves to nonstrictly hyperbolic systems.
strongly and nonstrictly hyperbolic systems
scientific article; zbMATH DE number 597450