122 citations · 221 across the 39 of their papers we have counts for
40 papers
Non-convergence of the principal eigenvalue of elliptic operators for large advection
Xueli Bai, Zhi-An Wang, Xin Xu +2
This paper investigates the limit of the principal eigenvalue as for the following elliptic equation \begin{align*} -Δφ(x)-2s\mathbf{v}\cdot\nablaφ(x)+c(x)φ(x)…
Infinitely many self-similar blow-up profiles for the Keller-Segel system in dimensions 3 to 9
Van Tien Nguyen, Zhi-An Wang, Kaiqiang Zhang
Based on the method of matched asymptotic expansions and Banach fixed point theorem, we rigorously construct infinitely many self-similar blow-up profiles for the parabolic-ellipti…
Effects and biological consequences of the predator-mediated apparent competition I: ODE models
Yuan Lou, Weirun Tao, Zhi-An Wang
This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the othe…
Convergence of boundary layers of chemotaxis models with physical boundary conditions~II: Non-degenerate
Guangyi Hong, Zhi-An Wang
This paper establishes the convergence of boundary-layer solutions of the consumption type Keller-Segel model with non-degenerate initial data subject to physical boundary conditio…
Boundary spike-layer solutions of the singular Keller-Segel system: existence, profiles and stability
Jose A. Carrillo, Jingyu Li, Zhi-An Wang +1
This paper is concerned with the boundary-layer solutions of the singular Keller-Segel model proposed by Keller-Segel (1971) in a multi-dimensional domain, where the zero-flux boun…
Convergence of boundary layers of chemotaxis models with physical boundary conditions I: degenerate initial data
Jose Antonio Carrillo, Guangyi Hong, Zhi-an Wang
The celebrated experiment of Tuval et al. \cite{tuval2005bacterial} showed that the bacteria living a water drop can form a thin layer near the air-water interface, where a so-call…
Global solvability and stability of an alarm-taxis system
Hai-Yang Jin, Zhi-An Wang, Leyun Wu
This paper is concerned with the global boundedness and stability of classical solutions to an alarm-taxis system describing the burglar alarm hypothesis as an important mechanism…
Coexistence of heterogenous predator-prey systems with density-dependent dispersal
De Tang, Zhi-An Wang
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome…
Novel Spatial Profiles of Population Distribution of Two Diffusive SIS Epidemic Models with Mass Action Infection Mechanism and Small Movement Rate for the Infected Individuals
Rui Peng, Zhi-an Wang, Guanghui Zhang +1
In this paper, we are concerned with two SIS epidemic reaction-diffusion models with mass action infection mechanism of the form , and study the spatial profile of population d…
Logistic damping effect in chemotaxis models with density-suppressed motility
Wenbin Lyu, Zhi-An Wang
This paper is concerned with a parabolic-elliptic chemotaxis model with density-suppressed motility and general logistic source in an -dimensional smooth bounded domain with Neu…
Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis
Qingqing Liu, Hongyun Peng, Zhi-An Wang
In this paper, we are concerned with a quasi-linear hyperbolic-parabolic system of persistence and endogenous chemotaxis modelling vasculogenesis in . Under some suitab…
A kinetic chemotaxis model with internal states and temporal sensing
Zhi-An Wang
By employing the Fourier transform to derive key a priori estimates for the temporal gradient of the chemical signal, we establish the existence of global solutions and hydrodynami…
Acceleration of Propagation in a chemotaxis-growth system with slowly decaying initial data
Zhi-An Wang, Wen-Bing Xu
In this paper, we study the spatial propagation dynamics of a parabolic-elliptic chemotaxis system with logistic source which reduces to the well-known Fisher-KPP equation without…
Asymptotic stability of diffusion waves of a quasi-linear hyperbolic-parabolic model for vasculogenesis
Qinging Liu, Hongyun Peng, Zhi-An Wang
In this paper, we derive the large-time profile of solutions to the Cauchy problem of a hyperbolic-parabolic system modeling the vasculogenesis in . When the initial data are…
Global classical solutions for a class of reaction-diffusion system with density-suppressed motility
Wenbin Lyu, Zhi-An Wang
This paper is concerned with a class of reaction-diffusion system with density-suppressed motility \begin{equation*} \begin{cases} u_{t}=Δ(γ(v) u)+αu F(w), & x \in Ω, \quad t>0, \\…
Asymptotic stability of exogenous chemotaxis systems with physical boundary conditions
Guangyi Hong, Zhian Wang
In this paper, we consider the exogenous chemotaxis system with physical mixed zero-flux and Dirichlet boundary conditions in one dimension. Since the Dirichlet boundary condition…
The uniform spreading speed in cooperative systems with non-uniform initial data
Ru Hou, Zhian Wang, Wen-Bing Xu +1
This paper considers the spreading speed of cooperative nonlocal dispersal system with irreducible reaction functions and non-uniform initial data. Here the non-uniformity means th…
Nonlinear stability of phase transition steady states to a hyperbolic-parabolic system modelling vascular networks
Guangyi Hong, Hongyun Peng, Zhi-An Wang +1
This paper is concerned with the existence and stability of phase transition steady states to a quasi-linear hyperbolic-parabolic system of chemotactic aggregation, which was propo…
Prescribing Gaussian curvature on surfaces with conical singularities and geodesic boundary
Luca Battaglia, Aleks Jevnikar, Zhi-An Wang +1
We study conformal metrics with prescribed Gaussian curvature on surfaces with conical singularities and geodesic boundary in supercritical regimes. Exploiting a variational argume…
Global boundedness of the fully parabolic Keller-Segel system with signal-dependent motilities
Zhi-An Wang, Jiashan Zheng
This paper establishes the global uniform-in-time boundedness of solutions to the following Keller-Setel system with signal-dependent diffusion and chemotaxis \begin{equation}\left…
Large Time Behavior and Diffusion Limit for a System of Balance Laws From Chemotaxis in Multi-dimensions
Tong Li, Dehua Wang, Fang Wang +2
We consider the Cauchy problem for a system of balance laws derived from a chemotaxis model with singular sensitivity in multiple space dimensions. Utilizing energy methods, we fir…
Travelling wave solutions of the density-suppressed motility model
Jing Li, Zhi-An Wang
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern format…
The Keller-Segel system with logistic growth and signal-dependent motility
Hai-Yang Jin, Zhi-An Wang
The paper is concerned with the following chemotaxis system with nonlinear motility functions \begin{equation}\label{0-1}\tag{} \begin{cases} u_t=\nabla \cdot (γ(v)\nabla u-…
Boundedness and asymptotics of a reaction-diffusion system with density-dependent motility
Hai-Yang Jin, Shijie Shi, Zhi-An Wang
We consider the initial-boundary value problem of a system of reaction-diffusion equations with density-dependent motility \begin{equation*}\label{e1}\tag{} \begin{cases} u_t…