We consider a hyperbolic system of first order obtained by reducing a conservative hyperbolic equation of second order in noncanonical form. We determine, generalizing a previous paper [1], the conditions for having a supplementary conservation law. As a particular case we obtain that the second order equation must be of Euler type with the usual conservation law for the energy.
In questa Nota si determina la classe delle equazioni conservative del secondo ordine di forma canonica che ammettono una equazione di conservazione supplementare, seguendo un procedimento dovuto a G. Boillat. Si ha occasione di illustrare il metodo su un esempio particolare.
In an earlier paper [1] we deduced the magneto-elastic system of equations in the three-dimensional case. The object of the present paper is to study the propagation of weak discontinuities associated with this system. We have occasion to compare results with other ones known in absence of magnetic field. In the last part of the paper we examine the case of small deformations obtaining the same results as in [8]
We characterize a set of second order hyperbolic conservative equations that are both compatible with a supplementary conservation law and completely exceptional.
We studied the propagation of first-order electromagnetic discontinuities through ferromagnetic materials whose magnetic permeability is a function of . We examined the condition for a discontinuity-wave not to generate a shock-wave (exceptionality conditions of Lax—Boillat). We found that the system is never fully exceptional, unless inthe plane wave case, if one supposes , or for with materials whose magnetic permeability solves a suitable differential equation.
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