  We investigate a relation between surface densities of star formation rate
(SFR) and stellar mass ($M_{*}$) at a $\sim 1$ kpc scale namely spatially
resolved star formation main sequence (SFMS) in massive
($\log(M_{*}/M_{\odot})>10.5$) face-on disc galaxies at $0.01<z<0.02$ and
$0.8<z<1.8$ and examine evolution of the relation. The spatially resolved SFMS
of $z\sim 0$ galaxies is discussed in a companion paper. For $z\sim 1$ sample,
we use 8 bands imaging dataset from CANDELS and 3D-HST and perform a
pixel-to-pixel SED fitting to derive the spatially resolved SFR and $M_{*}$. We
find a linear spatially resolved SFMS in the $z\sim 1$ galaxies that lie on the
global SFMS, while a 'flattening' at high $\Sigma_{*}$ end is found in that
relation for the galaxies that lie below the global SFMS. Comparison with the
spatially resolved SFMS of the $z\sim 0$ galaxies shows smaller difference in
the specific SFR (sSFR) at low $\Sigma_{*}$ than that at high $\Sigma_{*}$.
This trend is consistent with the evolution of the sSFR$(r)$ radial profile,
which shows a faster decrease in the central region than in the outskirt,
agrees with the inside-out quenching scenario. We then derive an empirical
model for the evolution of the $\Sigma_{*}(r)$, $\Sigma_{\rm SFR}(r)$ and
sSFR$(r)$ radial profiles. Based on the empirical model, we estimate the radial
profile of the quenching timescale and reproduce the observed spatially
resolved SFMS at $z\sim 1$ and $z\sim 0$.
