26 citations · 78 across the 10 of their papers we have counts for
11 papers
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…
Asymptotic profile of a two-dimensional chemotaxis--Navier--Stokes system with singular sensitivity and logistic source
Peter Y. H. Pang, Yifu Wang, Jingxue Yin
The chemotaxis--Navier--Stokes system \begin{equation*}\label{0.1} \left\{\begin{array}{ll} n_t+u\cdot \nabla n=\triangle n-χ\nabla\cdotp \left(\displaystyle\frac n {c}\nabla c\rig…
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…
Global solvability and stability to a nutrient-taxis model with porous medium slow diffusion
Chunhua Jin, Yifu Wang, Jingxue Yin
In this paper, we study a nutrient-taxis model with porous medium slow diffusion \begin{align*} \left\{ \begin{aligned} &u_t=Δu^m-χ\nabla\cdot(u\nabla v)+ξuv-ρu, \\ &v_t-Δv=-vu+μv(…
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…
Life Span of Solutions for a Semilinear Heat Equation with Initial Data Non-Rarefied at
Zhiyong Wang, Jingxue Yin
We study the Cauchy problem for a semilinear heat equation with initial data non-rarefied at . Our interest lies in the discussion of the effect of the non-rarefied factors…