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The main purpose of this paper is to estimate the thickness of boundary layer for nonlinear evolution equations with damping and diffusion as the diffusion parameter β goes to zero. We prove that the thickness of layer is of the order O(βγ)$O(\beta^{\gamma})$ with 0<γ<1$0<\gamma<1$, thus improving the corresponding result in (Ruan and Zhu in Discrete Contin. Dyn. Syst. 32(1) 331-352, 2012) where 0<γ<1/2$0<\gamma<1/2$ is obtained.

An estimate on the thickness of boundary layer for nonlinear evolution equations with damping and diffusion