摘要
本文研究通常Laplacian和分数次Laplacian的Allen-Cahn方程的行波解,以及方程在线性扰动情形下的行波速度的渐近公式,通过用非线性函数对行波解速度的估计,可以得到行波解的一致估计和解的导数在无穷远处的一致衰减估计,从而得到行波速度的渐近公式.
In this paper, we investigate the asymptotic formula of the speed of the traveling wave solutions to the Allen-Cahn equations under linear perturbations with the usual and fractional Laplacians. The key ingredient is to estimate the traveling speeds in terms of the potential function. By estimating the traveling speed in terms of the nonlinear potential function, we can get the uniform estimates of solutions and uniform decay of derivatives of solutions at infinity, which will give us the asymptotic formula for the traveling speeds.
出处
《中国科学：数学》
CSCD
北大核心
2016年第5期549-562,共14页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11371128)资助项目
