  We perform smoothed particle hydrodynamics (SPH) simulations for merging
binary carbon-oxygen (CO) white dwarfs (WDs) with masses of $1.1$ and $1.0$
$M_\odot$, until the merger remnant reaches a dynamically steady state. Using
these results, we assess whether the binary could induce a thermonuclear
explosion, and whether the explosion could be observed as a type Ia supernova
(SN Ia). We investigate three explosion mechanisms: a helium-ignition following
the dynamical merger (`helium-ignited violent merger model'), a carbon-ignition
(`carbon-ignited violent merger model'), and an explosion following the
formation of the Chandrasekhar mass WD (`Chandrasekhar mass model'). An
explosion of the helium-ignited violent merger model is possible, while we
predict that the resulting SN ejecta are highly asymmetric since its companion
star is fully intact at the time of the explosion. The carbon-ignited violent
merger model can also lead to an explosion. However, the envelope of the
exploding WD spreads out to $\sim 0.1R_\odot$; it is much larger than that
inferred for SN 2011fe ($< 0.1R_\odot $) while much smaller than that for SN
2014J ($\sim 1R_\odot$). For the particular combination of the WD masses
studied in this work, the Chandrasekhar mass model is not successful to lead to
an SN Ia explosion. Besides these assessments, we investigate the evolution of
unbound materials ejected through the merging process (`merger ejecta'),
assuming a case where the SN Ia explosion is not triggered by the helium- or
carbon-ignition during the merger. The merger ejecta interact with the
surrounding interstellar medium, and form a shell. The shell has a bolometric
luminosity of more than $2 \times 10^{35}$ ergs$^{-1}$ lasting for $\sim 2
\times 10^4$ yr. If this is the case, Milky Way should harbor about $10$ such
shells at any given time.
