  We study the singular limit problem referred to as the fast reaction limit.
This problem has been extensively studied when the same reaction term is used
in a two-component system. However, the behavior of the solution under
different reaction terms remains not yet well understood. In this paper, we
will consider the problem where the reaction term is represented by a power
term. We prove that the initial interface disappears immediately, and the
function converges to a solution that satisfies the heat equation.
