NGC 1042 is a late type bulgeless disk galaxy which hosts a low luminosity Active Galactic Nuclei (AGN) coincident with a massive nuclear star cluster. In this paper, we present the integral-field-spectroscopy (IFS) studies of this galaxy, based on the data obtained with the Mitchell spectrograph on the 2.7 meter Harlan J. Smith telescope. In the central $100textrm{-}300 mathrm{pc}$ region of NGC 1042, we find a circumnuclear ring structure of gas with enhanced ionization, which we suggest is mainly induced by shocks. Combining with the harmonic decomposition analysis of the velocity field of the ionized gas, we propose that the shocked gas is the result of gas inflow driven by the inner spiral arms. The inflow velocity is $sim 32pm10 mathrm{km} mathrm{s}^{-1}$ and the estimated mass inflow rate is $sim 1.1pm0.3 times 10^{-3} mathrm{M}_{odot} mathrm{yr}^{-1}$. The mass inflow rate is about one hundred times the blackholes mass accretion rate ($sim 1.4 times 10^{-5} mathrm{M}_{odot} mathrm{ yr}^{-1}$), and slightly larger than the star formation rate in the nuclear star cluster ($7.94 times 10^{-4} mathrm{M}_{odot} mathrm{yr}^{-1}$), implying that the inflow material is enough to feed both the AGN activity and the star formation in the nuclear star cluster. Our study highlights that secular evolution can be important in late-type unbarred galaxies like NGC 1042.
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