  The present study, on the expansion of universe, is based on an assumption
regarding the possibility of inter-conversion between matter and dark energy,
through some interaction of matter with the scalar field in the framework of
Brans-Dicke theory. The field equations for a spatially flat space-time have
been solved using an empirical dependence of scalar field parameter upon the
scale factor. To represent the behaviour regarding the non-conservation of
matter, a function, expressed in terms of the Hubble parameter, has been
empirically incorporated into the field equations. Their solution shows that,
this function, whose value is proportional to the matter content of the
universe, decreases monotonically with time. This matter-field interaction
generates late time acceleration, causing the deceleration parameter to change
its sign from positive to negative. Time dependence of the proportion of dark
energy component of the universe has been determined and shown graphically.
Time variation of gravitational constant and the Brans-Dicke dimensionless
parameter has been analyzed in the present study. The rate of generation of
dark energy from matter has been found to affect the time variations of
deceleration parameter and gravitational constant.
