中文摘要：

非线性发展方程渐近波速和行波解的存在性是发展方程理论研究中两个重要课题，周其具有强烈的实际背景和对数学理论提出的许多挑战性问题，正引起愈来愈多数学家的广泛关注．近30多年来，特别是近10年，对一些典型类型发展方程行波解及其相关的最小波速、渐近波速的理论研究得到了迅速发展，涌现出很多代表性的成果．本文力求总结这一领域的最新进展，向读者展示相关问题发展的背景、线索、脉络和重要的研究方法，以期待研究的进一步深入．

英文摘要：

The asymptotic speed of propagation and the existence of traveling solutions are two very important topics in the study of nonlinear evolution equations. Because of their strong backgrounds in applicable sciences such as physics and epidemics etc, and the interesting and challenging mathematical problems appearing in the study, they have been paid more and more attentions by the mathematicians and physicists. During the past thirty years, especially in the recent ten years, there are a great deal of excellent research results have been published on these two topics, and the theory has got developed. In this article, we present a short survey on the recent progress and development towards modeling, new results on the analysis of long-term behaviors about asymptotic speed of propagation, minimal wave speed and traveling wave solutions of some types of nonlinear evolution equations. We try to reveal the relative background, the idea, the developing clue and the researching techniques in order to motive the future research.