Periodic entropy solution to a conservation law with nonlocal source arising in radiative gas

We establish the global well-posedness and large-time asymptotic behaviour of spatially periodic entropy solutions to a scalar conservation law with nonlocal source arising in radiative gas. The global existence is established by the L1-contraction and the comparison principle for the vanishing viscosity approximation. Moreover, we show that if the initial data is periodic, the source term induces the solution to decay in L2-norm at an exponential rate to the mean value of initial data over one space period.