Exponential decay for Kirchhoff wave equation with nonlocal condition in a noncylindrical domain

In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the Kirchhoff wave equation with nonlocal condition and weak damping u t t − M ( | | ▽ u | | 2 2 ) Δ u + ∫ 0 t g ( t − s ) Δ u ( ⋅ , s ) d s + α u t = 0 , i n Q ^ , where Q ^ is a noncylindrical domain of R n + 1 (n ≥ 1) with the lateral boundary ∑ ^ and α is a positive constant.