On a Class of Balance Laws with Absorption: Support Properties and Finite-Time Extinction

We consider the Cauchy problem ut + 1m (um)x = −up in (0, +∞) × R,u = u0 in {0} × R, where 0 < m < 1, p > 0, and u0 has compact support. Studying the Riemann problem and using comparison results we obtain estimates of the support of the unique nonnegative entropy solution for any positive time. The decay of the solution is also investigated.