The author studies systems of balance laws in \(m\) space dimensions with physical viscosity, i.e. hyperbolic-parabolic systems of the form \[ w_t + \sum_{i=1}^m f_i(w)_{x_i} = \sum_{i,j=1}^m \left[ B_{ij}(w) w_{x_j}\right]_{x_i} + r(w) \] for initial conditions which are sufficiently close to a constant equilibrium state in \(H^s\) for some \(s>\frac{m}{2}+1\). Under some additional assumptions, in particular the existence of a normal form which separates the hyperbolic and the parabolic part and the Kawashima-Shizuta condition she proves the existence of a unique global solution for the Cauchy problem. While there might be also a splitting into conservation laws and balance laws this splitting does not have to be related to the hyperbolic-parabolic normal form.
The result is proved using the energy method where the different parts in the solution are separated according to their decay properties. The main theorem includes as special cases previous results on global existence for hyperbolic-parabolic conservation laws with small initial data and for hyperbolic balance laws.
To illustrate the strength of the main theorem, it is applied to a model of physical gas dynamics that contains several dissipation parameters and both translational and vibrational non-equilibrium.