Van der Waals方程是一类重要的非线性偏微分方程,能够描述非弹性碰撞粒子流的动力学行为。本文证明了在充分小色散情况下,具有五阶色散项的Van der Waals方程波前解的持续存在性。首先,由于其波前解实际对应三维空间的异宿轨,利用辐角...Van der Waals方程是一类重要的非线性偏微分方程,能够描述非弹性碰撞粒子流的动力学行为。本文证明了在充分小色散情况下,具有五阶色散项的Van der Waals方程波前解的持续存在性。首先,由于其波前解实际对应三维空间的异宿轨,利用辐角原理计算了其平衡点的稳定和不稳定流形的维数。其次,由于三维空间异宿轨的存在性研究是一个困难的问题,利用几何奇异摄动理论证明慢系统的临界流形是法向双曲的,进而把三维问题转化为二维问题。最后,在未扰动系统存在异宿轨的情况下,利用隐函数定理证明扰动系统的稳定流形与不稳定流形横截相交,即异宿轨的持续存在性。展开更多
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a...This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.展开更多
This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we estab...This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we establish the existence of pyra- midal traveling fronts.展开更多
This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spa...This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.展开更多
直流输电线路单端量保护不能实现绝对选择性,对于纵联保护,需要考虑故障暂态时的电容电流和两侧采样数据的同步性。区外故障时直流输电线路满足行波特征不变性,线路两侧波形的相似度高,区内故障破坏了行波特征不变性,线路两侧波形的相...直流输电线路单端量保护不能实现绝对选择性,对于纵联保护,需要考虑故障暂态时的电容电流和两侧采样数据的同步性。区外故障时直流输电线路满足行波特征不变性,线路两侧波形的相似度高,区内故障破坏了行波特征不变性,线路两侧波形的相似度低,由此提出一种基于改进动态时间弯曲(dynamic time warping,DTW)的行波波形相似性的高压直流输电线路保护方案。DTW算法通过对时间轴的伸缩,实现2个序列的动态匹配,具有良好的耐同步特性。基于改进DTW的保护方案,在启动判据启动后,计算线路两侧故障行波波形之间的改进动态时间弯曲距离,建立识别直流线路区内外故障的判据。仿真结果表明,该算法能够准确识别区内外故障,不存在保护死区,具有较好的耐同步性,耐受过渡电阻能力强,具有一定的抗噪声和抗异常数据的能力。展开更多
文摘Van der Waals方程是一类重要的非线性偏微分方程,能够描述非弹性碰撞粒子流的动力学行为。本文证明了在充分小色散情况下,具有五阶色散项的Van der Waals方程波前解的持续存在性。首先,由于其波前解实际对应三维空间的异宿轨,利用辐角原理计算了其平衡点的稳定和不稳定流形的维数。其次,由于三维空间异宿轨的存在性研究是一个困难的问题,利用几何奇异摄动理论证明慢系统的临界流形是法向双曲的,进而把三维问题转化为二维问题。最后,在未扰动系统存在异宿轨的情况下,利用隐函数定理证明扰动系统的稳定流形与不稳定流形横截相交,即异宿轨的持续存在性。
基金Supported by the National Natural Science Foundation of China(No.19971032)the second author is supported by Natural Science Foundation of Canadaby a Petro Canada Young Innovator Award.
文摘This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of ＂desirable pair of upper-lower solutions＂, through which a subset can be constructed. We then apply the Schauder＇s fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.
基金supported by NNSF of China(11071105,11371179)the Program for New Century Excellent Talents in University(NCET-10-0470)
文摘This paper is concerned with nonplanar traveling fronts for delayed reaction- diffusion equation with bistable nonlinearity in RTM （m〉 3）. By the comparison principle and super- and subsolutions technique, we establish the existence of pyra- midal traveling fronts.
基金Supported by the National Natural Science Foundation of China (10961017)
文摘This paper is concerned with travelling front solutions to a vector disease model with a spatio-temporal delay incorporated as an integral convolution over all the past time up to now and the whole one-dimensional spatial domain R.When the delay kernel is assumed to be the strong generic kernel,using the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.
文摘直流输电线路单端量保护不能实现绝对选择性,对于纵联保护,需要考虑故障暂态时的电容电流和两侧采样数据的同步性。区外故障时直流输电线路满足行波特征不变性,线路两侧波形的相似度高,区内故障破坏了行波特征不变性,线路两侧波形的相似度低,由此提出一种基于改进动态时间弯曲(dynamic time warping,DTW)的行波波形相似性的高压直流输电线路保护方案。DTW算法通过对时间轴的伸缩,实现2个序列的动态匹配,具有良好的耐同步特性。基于改进DTW的保护方案,在启动判据启动后,计算线路两侧故障行波波形之间的改进动态时间弯曲距离,建立识别直流线路区内外故障的判据。仿真结果表明,该算法能够准确识别区内外故障,不存在保护死区,具有较好的耐同步性,耐受过渡电阻能力强,具有一定的抗噪声和抗异常数据的能力。
