Stability under a variational convergence of nonlinear time delays reaction-diffusion equations is discussed. Problems considered cover various models of population dynamics or diseases in heterogeneous environments where delays terms may depend on the space variable. As a consequence a stochastic homogenization theorem is established and applied to vector disease and logistic models. The results illustrate the interplay between the growth rates and the time delays which are mixed in the homogenized model.

中文翻译：

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一类非线性时滞反应扩散方程的收敛性

讨论了非线性时滞反应扩散方程的变收敛解的稳定性。所考虑的问题涵盖了异质环境中的各种人口动态或疾病模型，其中延迟项可能取决于空间变量。结果，建立了随机均化定理，并将其应用于媒介疾病和逻辑模型。结果说明了均质模型中混合了增长率和时间延迟之间的相互作用。