  In the one-loop approximation we derive the equation of motion for a
classical scalar field \phi_c (t) with the back reaction of particle production
included. Renormalization of mass and couplings of \phi_c is done explicitly.
The equation is non-local in time, but can easily be treated perturbatively or
numerically. For the weak trilinear coupling of the external field to the
produced particles, the new equation gives the same solution as the familiar
one with the \Gamma \phi_c term. For a stronger coupling and other types of
couplings the results are significantly different. The equation can be applied
to the universe heating by the inflaton decay and to spontaneous baryogenesis.
