  In $2011$, Herzog, Hibi, and Ohsugi conjectured that if $J$ is the cover
ideal of a chordal graph, then $J^s$ is componentwise linear for all $s \ge 1.$
In 2022, H\`a and Tuyl considered objects more general than chordal graphs and
posed the following problem: Let $J(\Delta)$ be the cover ideal of a simplicial
tree $\Delta.$ Is it true that $J(\Delta)^s$ is componentwise linear for all $s
\geq 1$? In this article, we give an affirmative answer to this problem.
