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Motivated by biological aspects related to fungus growth, we consider thecompetition of growth and corrosion. We study a modification of the totallyasymmetric exclusion process, including the probabilities of injection $\alpha$and death of the last particle $\delta$. The system presents a phase transitionat $\delta_c(\alpha)$, where the average position of the last particle $<L>$grows as $\sqrt{t}$. For $\delta>\delta_c$, a non equilibrium stationary stateexists while for $\delta<\delta_c$ the asymptotic state presents a low densityand max current phases. We discuss the scaling of the density and currentprofiles for parallel and sequential updates.

Dynamical phase transition of a 1D transport process including death