Solvability of matrix Riccati equations

Abstract

The paper is aimed at studying solvability conditions for the quadratic matrix Riccati equation that arises in connection with the Chapman-Enskog projection for the Cauchy problem and the mixed problem for moment approximations of kinetic equations. The structure of the matrix equation allows for the formulation of necessary and sufficient conditions for the existence of solutions in terms of eigenvectors and associated vectors of the coefficient matrix. © 2009 Springer Science+Business Media, Inc.