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.