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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