on the annihilator of local cohomology

Let $r$ be a commutative noetherian ring, $a$ an ideal of $r$, $m$ a finitely generated $r$-module and $t$ a nonnegative integer. ##in certain cases, we give some bounds under inclusion for the annihilator of $h^t_{a}(m)$ in terms of minimal primary decomposition of the zero submodule of $m$, which are independent of the choice of minimal primary decomposition. ##then, by using those bounds, we compute the annihilators of local cohomology modules in certain cases.