Exact internal controllability of nodal profile for first order quasilinear hyperbolic systems

For 1-D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of semi-global C1 solution, by means of the results on both the exact boundary controllability and the exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be obtained purely with the help of internal controls. Moreover, using a perturbation method, by adding suitable internal controls to the part of equations corresponding to zero eigenvalues, the corresponding exact internal controllability of nodal profile for 1-D first order quasilinear hyperbolic systems with zero eigenvalues can be also obtained.