Nonlinear Stability of Traveling Wavefronts for a Discrete Cooperative Lotka-Volterra System With Delays北大核心CSCD

The stability of traveling wave solutions of the reaction diffusion model is a very important research topic. The globally nonlinear stability of traveling wavefronts for a discrete cooperative Lotka-Volterra system with delays was studied. More precisely, for the initial perturbation decaying exponentially to the traveling wavefronts with a relatively large speed at infinity, but arbitrarily large speeds in other positions, by means of the L2⁃ weighted energy method, the comparison principle and the squeezing technique, such traveling wavefronts were obtained and proved to be of exponentially asymptotic stability. Moreover, the problem of establishing the energy estimates was solved under the actions of the discrete dispersal operator and the time delays. In short, the extension of the weighted energy method to discrete systems with delays, enriches the relative research. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

一类随机非自伴波方程的半离散有限元近似

本文研究了由白噪音驱动的随机非自伴波方程的有限元近似,由于线性算子A非自伴,不能应用A的特征值和特征向量,从而得到的结果更具有一般性.空间离散上采用标准的有限元法,并借助强连续算子函数的性质,得到了该方程的强收敛误差估计.本文方法也适用于多维情况的分析.最后用数值算例验证了理论分析的正确性.