  We consider the Cauchy problem for a system of balance laws derived from a
chemotaxis model with singular sensitivity in multiple space dimensions.
Utilizing energy methods, we first prove the global well-posedness of classical
solutions to the Cauchy problem when only the energy of the first order spatial
derivatives of the initial data is sufficiently small, and the solutions are
shown to converge to the prescribed constant equilibrium states as time goes to
infinity. Then we prove that the solutions of the fully dissipative model
converge to those of the corresponding partially dissipative model when the
chemical diffusion coefficient tends to zero.
