An estimate on the thickness of boundary layer for nonlinear evolution equations with damping and diffusion
Wenshu Zhou, Xulong Qin, Xiaodan Wei · Journal of Inequalities and Applications · 2016
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 $O(\beta^{\gamma})$ with $0<\gamma<1$ , thus improving the corresponding result in (Ruan and Zhu in Discrete Contin. Dyn. Syst. 32(1) 331-352, 2012) where $0<\gamma<1/2$ is obtained.