Global BV Solutions of Compressible Euler Equations with Spherical Symmetry and Damping

In this paper, we study the global existence of BV solutions for compressible Euler equations with spherical symmetry and damping, using Glimmʹs scheme. The key point to consider is the combination of the geometric effects due to the spherical symmetry and the effects of the frictional damping on the total variation of the solutions. By measuring the strength of the waves byr-s, where (r, s) are the Riemann invariants, we construct a function which leads to the boundedness of the BV norm of the corresponding approximate solutions.