几类积分微分方程的行波解与渐近传播速度研究

渐近传播速度与行波解是描述空间传播动力学的两个重要概念，在物理，化学，生态学，疾病学等领域有着重要的应用价值。研究渐近传播速度，行波解及相关性质是当前热门的课题。本项目主要研究几类源于实际问题的积分微分方程的行波解与渐近传播速度。具体为带退化非线性的积分微分方程，非线性决定积分微分方程和非单调积分微分方程。我们将通过发展一些方法技巧，建立这些积分微分方程行波解的性质（比如单调性，渐近性，唯一性）和渐近传播速度。

The asymptotic speed of spread and the traveling wave solution are two important concepts to describe the dynamics of spatial propagation, and have important application value in the fields of physics, chemistry, ecology and disease. It is a hot topic to study the spreading speed, traveling wave solution and its related properties. This project is mainly devoted to the study of spreading speed and traveling wave solution of some integro-differential equations. Specifically, we consider the integro-differential equation with degenerate nonlinearity, nonlinear determine integro-differential equation and non-monotone integro-differential equation. We will develop some methods and techniques to establish the properties of traveling wave solutions (such as monotonicity, asymptotic behavior, and uniqueness) and the spreading speed for these equations.