Associate primes of local cohomology modules over certain quotients of regular rings

Let $R$ be a regular ring containing a field $k$. Let $\mathbf{x}=x_1,\dots ,x_r$ be a regular sequence in $R$ such that $R\mathrm{/}(\mathbf{x})$ is a regular ring. Fix $m\ge 1$. Set $A_m=R\mathrm{/}(\mathbf{x}{)}^m$. We show that for any ideal $Q$ of $A_m$ the set $\text{Ass }{H}_Q^i(A_m)$ is a finite set for $i\ge 0$, in the following cases: 1. $\text{char }k=p>0$. 2. $\text{char }k=0$, $R$ is local or a smooth affine algebra over $k$.