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Solvability of matrix Riccati equations. (English. Russian original) Zbl 1182.15009
J. Math. Sci., New York 163, No. 2, 176-187 (2009); translation from Tr. Semin. Im. I. G. Petrovskogo 27, No. 2, 281-300 (2009).
Summary: 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.

MSC:
15A24 Matrix equations and identities
35L03 Initial value problems for first-order hyperbolic equations
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