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In this paper, the large time behavior of solutions of 1-D isentropicNavier-Stokes system is investigated. It is shown that a composite waveconsisting of two viscous shock waves is stable for the Cauchy problem providedthat the two waves are initially far away from each other. Moreover thestrengths of two waves could be arbitrarily large.

Stability of a Composite Wave of Two Seperate Strong Viscous Shock Waves for 1-D Isentropic Navier-Stokes System