Discussion

5.7 Discussion

So as to anticipate a possible misunderstanding I remark that the equations (93

, 94

, 95

) with $AABA$ 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 $Λ$ are used as variables. But (93

, 94

, 95

, 89

, 91

) are equations for the physical variables $A AB A ,A$ or in fact $A AB n, T,U ,t$ , and $A q$ . 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 ].