  For backward stochastic Volterra integral equations (BSVIEs, for short),
under some mild conditions, the so-called adapted solutions or adapted
M-solutions uniquely exist. However, satisfactory regularity of the solutions
is difficult to obtain in general. Inspired by the decoupling idea of
forward-backward stochastic differential equations, in this paper, for a class
of BSVIEs, a representation of adapted M-solutions is established by means of
the so-called representation partial differential equations and (forward)
stochastic differential equations. Well-posedness of the representation partial
differential equations are also proved in certain sense.
