122 citations · 329 across the 14 of their papers we have counts for
14 papers
On a cross-diffusive SIS epidemic model with power-like nonlinear incidence
Huicong Li, Tian Xiang
In this work, we study global existence, boundedness and convergence of nonnegative classical solutions of a Neumann initial-boundary value problem for a cross diffusive SIS (susce…
Global solvability in a two-species chemotaxis system with signal production
Guoqiang Ren, Tian Xiang
In this work, we study the Neumann initial-boundary value problem for a two-species chemotaxis system with Lotka-Volterra competition and signal production. Under a rather weak and…
Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimensions
Jiawei Chu, Haiyang Jin, Tian Xiang
In this work, we study the Neumann initial boundary value problem for a three-component chemotaxis model in any dimensional bounded and smooth domains; this model is used to descri…
Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption
Guoqiang Ren, Tian Xiang
In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for a two-species chemotaxis consumption model in a bounded smooth but…
Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model
Hai-Yang Jin, Tian Xiang
In this work, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a combined chemotaxis-haptotaxis mod…
A new result for 2D boundedness of solutions to a chemotaxis--haptotaxis model with/without sub-logistic source
Tian Xiang, Jiashan Zheng
We consider the Neumann problem for a coupled chemotaxis-haptotaxis model of cancer invasion with/without kinetic source in a 2D bounded and smooth domain. For a large class of cel…
On boundedness, gradient estimate, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop
Ke Lin, Tian Xiang
In this work, we study dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model wi…
Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model
Hai-Yang Jin, Tian Xiang
In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded d…
Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system
Tian Xiang
It is well-known that the Neumann initial-boundary value problem for the minimal-chemotaxis-logistic system in a 2D bounded smooth domain has no blow-up for any choice of parameter…
Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics
Hai-Yang Jin, Tian Xiang
In this paper, we study the rates of convergence of supposedly given global bounded classical solutions to a two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competi…
Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion
Huicong Li, Rui Peng, Tian Xiang
This paper is concerned with two frequency-dependent SIS epidemic reaction-diffusion models in heterogeneous environment, with a cross-diffusion term modeling the effect that susce…
How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system?
Tian Xiang
In this paper, we study the minimal Keller-Segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and o…
Boundedness and exponential convergence of a chemotaxis model for tumor invasion
Haiyang Jin, Tian Xiang
We revisit the following chemotaxis system modeling tumor invasion \begin{equation*} \begin{cases} u_t=Δu-\nabla \cdot(u\nabla v),& x\inΩ, t>0,\\ v_t=Δv+wz,& x\inΩ, t>0,\\ w_t=-wz,…
A class of chemotaxis systems with growth source and nonlinear secretion
Zhi-an Wang, Tian Xiang
In this paper, we are concerned with a class of parabolic-elliptic chemotaxis systems encompassing the prototype $$\left\{\begin{array}{lll} &u_t = \nabla\cdot(\nabla u-χu\nabla v)…