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For the p-system with large BV initial data, an assumption introduced in [3]by Bakhvalov guarantees the global existence of entropy weak solutions withuniformly bounded total variation. The present paper provides a partialconverse to this result. Whenever Bakhvalov's condition does not hold, we showthat there exist front tracking approximate solutions, with uniformly positivedensity, whose total variation becomes arbitrarily large. The constructionextends the arguments in [4] to a general class of pressure laws.

No BV bounds for approximate solutions to p-system with general pressure law