The effect of noise intensity on parabolic equations
Guangying Lv, Hui Gao, Jinlong Wei, Jiang-Lun Wu · Discrete and Continuous Dynamical Systems - B · 2019
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.