So as to anticipate a possible misunderstanding I remark that the equations (93, 94, 95) with
from (89) and (91) are neither symmetric nor fully hyperbolic. Indeed the underlying symmetry of the
system (79, 80, 81), and (84) reveals itself only when the Lagrange multipliers are used as
variables. But (93, 94, 95, 89, 91) are equations for the physical variables or in fact
, and . Also the hyperbolicity in the whole state space is lost, because the
equations (89, 90) are restricted to linear terms. Therefore the system is hyperbolic only in the
neighbourhood of equilibrium. For a more detailed discussion of these aspects, see Müller &
Ruggeri [39, 40].