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# Large BV solutions to Euler equations in the isothermal self-gravitating gases with damping

• The present paper gives the global existence of $BV$ solutions to the radial motions of self-gravitating gases with damping. We construct approximate solutions by a modified Glimm scheme, considering the effects of the geometric source term, the integrand term, and the damping term at the same time. With the strength of the waves measured by $|\Delta(w-z)|$, where $(w,z)$ are the Riemann invariants to the corresponding Euler equations, we prove that the $BV$ norms of the approximate solutions are bounded.
Mathematics Subject Classification: Primary: 35L65, 76N10; Secondary: 65M12.

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