  In this work we study the existence, uniqueness and polynomial stability of
the pseudo almost periodic mild solutions of semi-linear diffusion equations
with rough coefficients in certain interpolation spaces. First, we rewirte the
equations in abstract parabolic equation. Then, we use the polynomial stability
of the semigroups of the corresponding linear equations to prove the
boundedness of the solution operator for the linear equations in appropriate
interpolation spaces. We show that this operator preserves the pseudo almost
periodic property of functions. We will use the fixed point argument to obtain
the existence and stability of the pseudo almost periodic mild solutions for
the semi-linear equations. The abstract results will be applied to the
semi-linear diffusion equations with rough coefficients to obtain our desired
results.
