Zero-relaxation and vanishing-damping limits of pressureless Euler system

We are concerned with the one-dimensional pressureless Euler system with relaxation in the Radon measure space. As the relaxation time tends to zero, the entropy solution converges to a static solution with the density converging to its initial value. As the relaxation time tends to infinity, which means the damping vanishes, the entropy solution of damped pressureless Euler system converges to that of pressureless Euler system.