Context : The detection of a narrow SiO line emission toward the young shocks of the L1448-mm outflow has been interpreted as a signature of the magnetic precursor of C-shocks .
In contrast with the very low SiO abundances ( \leq 10 ^ { -12 } ) derived from the ambient gas , the narrow SiO emission in the precursor component at almost ambient velocities reveals enhanced SiO abundances of \sim 10 ^ { -11 } .
This enhancement has been proposed to be produced by the sputtering of the grain mantles at the very first stages of C-shocks .
However , modelling of the sputtering of grains has usually averaged the SiO abundances over the dissipation region of C-shocks , which can not explain the recent observations .

Aims : To model the evolution of the gas phase abundances of molecules like SiO , CH _ { 3 } OH and H _ { 2 } O , produced by the sputtering of the grain mantles and cores as the shock propagates through the ambient gas .
We consider different initial gas densities and shock velocities .

Methods : We propose a parametric model to describe the physical structure of C-shocks as a function of time .
Using the known sputtering yields for water mantles ( with other minor constituents like silicon and CH _ { 3 } OH ) and olivine cores by collisions with H _ { 2 } , He , C , O , Si , Fe and CO , we follow the evolution of the abundances of silicon , CH _ { 3 } OH and H _ { 2 } O ejected from grains along the evolution of the shock .

Results : The evolution of the abundances of the sputtered silicon , CH _ { 3 } OH and H _ { 2 } O shows that CO seems to be the most efficient sputtering agent in low velocity shocks .
The velocity threshold for the sputtering of silicon from the grain mantles is appreciably reduced ( by 5-10 km s ^ { -1 } ) by CO compared to other models .
The sputtering by CO can generate SiO abundances of \sim 10 ^ { -11 } at the early stages of low velocity shocks , consistent with those observed in the magnetic precursor component of L1448-mm .
Our model satisfactorily reproduce the progressive enhancement of SiO , CH _ { 3 } OH and H _ { 2 } O observed in this outflow , suggesting that this enhancement may be due to the propagation of two shocks with v _ { s } =30 km s ^ { -1 } and v _ { s } =60 km s ^ { -1 } coexisting within the same region .

Conclusions : Our simple model can be used to estimate the time dependent evolution of the abundances of molecular shock tracers like SiO , CH _ { 3 } OH , H _ { 2 } O or NH _ { 3 } in very young molecular outflows .