On the Stanley depth of powers of some classes of monomial ideals

Given arbitrary monomial ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $K$, we investigate the Stanley depth of powers of the sum $I+J$, and their quotient rings, in $A{\otimes }_{K}B$ in terms of those of $I$ and $J$. Our results can be used to study the asymptotic behavior of the Stanley depth of powers of a monomial ideal. For instance, we solved the case of monomial complete intersection.