The symmetry energy at finite temperature and the constraint on it from heavy ion collisions

we present the symmetry energies for nuclear matter at finite temperature calculated by means of the thermodynamics with Skyrme energy density functional. We also present the ImQMD05 model analysis of the experimental data for the double n/p ratio and the isospin diffusion data for 112,124Sn+112,124Sn and the consistent constraint on the density dependence of the potential symmetry energy is obtained.