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We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulkspacetime with a variable equation of state for the fluid presented on theshell. In such a fluid the angular pressure $p$ is a function of both surfaceenergy density $\sigma $ and the radius $R$ of the thin-shell. Explicit casesof the thin shells connecting two non-identical cloud of strings spacetimes anda flat Minkowski spacetime to the Schwarzschild metric are investigated.

Stability of spherically symmetric timelike thin-shells in general relativity with a variable equation of state