Several applications for systems of conservation laws of the form $U_{t} + (\Phi (U) U)_{x} =0$ , $U: R_{t}\times R_{x}\rightarrow R^{n}$ , $n\geq 2$ , with $\Phi (U) = \phi (r, \Theta ): R^{n}\rightarrow R$ , $r = |U|$ , and $\Theta = U/|U|\in S^{n-1}$ , are obtained by imposing structural conditions to provide a classification framework for solutions dependent on the form of $\phi (U)$ . By prescribing the evolution of a particular eigenvalue, we can categorize classes of such functions, $\phi $ , for which this evolution is met, into depending on either a scalar field $z=rK(\Theta )$ , where $K: S^{n-1}\rightarrow R$ , or on the vector field $\Theta $ , and find for which the amplitude of solutions may blow up in finite time. As a consequence, solutions to the corresponding Riemann problems can be divided into those with are classical and those which involve delta-shocks and/or vacuum states.
