# American Institute of Mathematical Sciences

July  2009, 8(4): 1451-1467. doi: 10.3934/cpaa.2009.8.1451

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

 1 Department of Mathematics, Shanghai University, Shanghai, 200444, China, China

Received  March 2008 Revised  January 2009 Published  March 2009

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.
Citation: Yulan Xu, Yanping Dou. Large BV solutions to Euler equations in the isothermal self-gravitating gases with damping. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1451-1467. doi: 10.3934/cpaa.2009.8.1451
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