26 citations · 77 across the 15 of their papers we have counts for
8 papers · 1 filter
Critical Sharp Front for Doubly Nonlinear Degenerate Diffusion Equations with Time Delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
This paper is concerned with the critical sharp traveling wave for doubly nonlinear diffusion equation with time delay, where the doubly nonlinear degenerate diffusion is defined b…
Propagation speed of degenerate diffusion equations with time delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020…
A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion
Shanming Ji, Zhian Wang, Tianyuan Xu +1
This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling wa…
Variational Approach of Critical Sharp Front Speeds in Density-dependent Diffusion Model with Time Delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.}…
Sharp, Smooth, and Oscillatory Traveling Waves of Degenerate Diffusion Equation with Delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
We consider the non-monotone degenerate diffusion equation with time delay. Different from the linear diffusion equation, the degenerate equation allows for semi-compactly supporte…
Theoretical and numerical studies on global stability of traveling waves with oscillations for time-delayed nonlocal dispersion equations
Tianyuan Xu, Shanming Ji, Rui Huang +2
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically…
Propagating Profiles of a Chemotaxis Model with Degenerate Diffusion: Initial Shrinking, Eventual Smoothness and Expanding
Tianyuan Xu, Shanming Ji, Ming Mei +1
We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect…
Early and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms
Tianyuan Xu, Shanming Ji, Chunhua Jin +2
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migrati…