The effect of noise intensity on parabolic equations

In this paper, the effect of noise intensity on parabolic equations is considered. We focus on the effect of noise on the energy solutions of stochastic parabolic equations. By utilising Ito's formula and the energy estimate method, we obtain excitation indices of the solution $ u $ at time $ t $. Furthermore, we improve existing results by introducing a simple method to verify the existing results in the literature.