5.7 Discussion

So as to anticipate a possible misunderstanding I remark that the equations (93View Equation, 94View Equation, 95View Equation) with AABA from (89View Equation) and (91View Equation) are neither symmetric nor fully hyperbolic. Indeed the underlying symmetry of the system (79View Equation, 80View Equation, 81View Equation), and  (84View Equation) reveals itself only when the Lagrange multipliers Λ are used as variables. But (93View Equation, 94View Equation, 95View Equation, 89View Equation, 91View Equation) 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 (89View Equation, 90View Equation) 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 [3940].


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