A variational formulation of symmetric systems of conservation laws (Q2716455)

Consider the nonlinear systems of conservation laws which admits an entropy density of the form: NEWLINE\[NEWLINE \sum_{i=1}^{n}\frac{\partial}{\partial x_i}(\frac{\partial \Phi _i} {\partial z_j})=0,\quad j=1,\dots,n, \tag{1} NEWLINE\]NEWLINE where \(x\in\Omega\subset \mathbb{R}^m\), \(z:\Omega\to \mathbb{R}^n\), and \(\Phi: \mathbb{R}^n\to \mathbb{R}^m\) is a given smooth map. The author obtains the weak form of system (1) from a variational principle. This approach permits a simplified treatment of the symmetry group for such systems. For such point of view specially is examined the case of hyperbolic systems.