Entropy and global existence for hyperbolic balance laws
The paper is concerned with multidimensional systems of balance laws \[ U_t+\sum\limits_{j=1}^d F_j(U)_{x_j}=Q(U), \quad U=U(x,t), \quad (x,t)\in {\mathbb R}^d\times [0,+\infty). \] Under some structural conditions, including the entropy dissipation condition and the Kawashima condition, the author proves existence and stability of global smooth solutions with initial data close to a constant equilibrium state. It is also shown that the Kawashima condition reduces to the known Kawa\-shima condition for the hyperbolic-parabolic systems derived through the Chapman-Enskog expansion. Applications to Bouchut's discrete velocity BGK models are given.
scientific article; zbMATH DE number 2113851