arXiv subjects

Xueping Li

Publications and source records attributed to Xueping Li.

26 records · Page 2Linked to original sources

arXiv2024

Longtime behaviors of an epidemic model with nonlocal diffusions and a free boundary: spreading-vanishing dichotomy

We propose a nonlocal epidemic model whose spatial domain evolves over time and is represented by $[0,h(t)]$ with $h(t)$ standing for the spreading front of epidemic. It is assumed that the agents can cross the fixed boundary $x=0$, but they will die immediately if they do it, which implies that the area $(-\infty,0)$ is a hostile environment for the agents. We first show that this model is well posed, then prove that the longtime behaviors are governed by a spreading-vanishing dichotomy and finally give some criteria determining spreading and vanishing. Particularly, we obtain the asymptotical behaviors of the principal eigenvalue of a cooperative system with nonlocal diffusions without assuming the related nonlocal operator is self-adjoint, and the steady state problem of such cooperative system on half space $[0,\infty)$ is studied in detail.

math.AP↗

arXiv2024

Assessing the Effects of Container Handling Strategies on Enhancing Freight Throughput

As global supply chains and freight volumes grow, the U.S. faces escalating transportation demands. The heavy reliance on road transport, coupled with the underutilization of the railway system, results in congested highways, prolonged transportation times, higher costs, and increased carbon emissions. California's San Pedro Port Complex (SPPC), the nation's busiest, incurs a significant share of these challenges. We utilize an agent-based simulation to replicate real-world scenarios, focusing on the intricacies of interactions in a modified intermodal inbound freight system for the SPPC. This involves relocating container classification to potential warehouses in California, Utah, Arizona, and Nevada, rather than exclusively at port areas. Our primary aim is to evaluate the proposed system's efficiency, considering cost and freight throughput, while also examining the effects of workforce shortages. Computational analysis suggests that strategically installing intermodal capabilities in select warehouses can reduce transportation costs, boost throughput, and foster resour

cs.MA↗

arXiv2024

Dynamics for a diffusive epidemic model with a free boundary: sharp asymptotic profile

This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition, respectively. The longtime behaviors has been proved to be governed by a spreading-vanishing dichotomy in \cite{LL}, and when spreading happens, the spreading speed is determined in \cite{LLW}. In this paper, by constructing some subtle upper and lower solutions, as well as employing some detailed analysis, we improve the results in \cite{LLW} and obtain the sharp asymptotic spreading profiles, which show the homogeneous Dirichlet boundary condition and Neumann boundary condition imposed at the fixed boundary $x=0$ lead to the same asymptotic behaviors of $h(t)$ and $(u,v)$ near the spreading front $h(t)$.

math.AP↗

arXiv2024

Dynamics for a diffusive epidemic model with a free boundary: spreading speed

We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann condition, respectively. A spreading-vanishing dichotomy and some sharp criteria were obtained in \cite{LL}. In this paper, when spreading happens, we not only obtain the exact spreading speed of the spreading front described by the right boundary, but derive some sharp estimates on the asymptotical behavior of solution component $(u,v)$. Our arguments depend crucially on some detailed understandings for a corresponding semi-wave problem and a steady state problem.

math.AP↗

arXiv2024

The free boundary problem of an epidemic model with nonlocal diffusions and nonlocal reactions: spreading-vanishing dichotomy

This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and the infective rate of humans are represented by nonlocal reaction terms. Thus our model has four integral terms which bring some diffculties for the study of the corresponding principal eigenvalue problem. Firstly, using some elementray analysis instead of Krein-Rutman theorem and the variational characteristic, we obtain the existence and asymptotic behaviors of principal eigenvalue. Then a spreading-vanishing dichotomy is proved to hold, and the criteria for spreading and vanishing are derived. Lastly, comparing our results with those in the existing works, we discuss the effect of nonlocal reaction term on spreading and vanishing, finding that the more nonlocal reaction terms a model has, the harder spreading happens.

math.AP↗

arXiv2024

Dynamics for a diffusive epidemic model with a free boundary: spreading-vanishing dichotomy

This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and lower solutions method and the regularity theory, we first study some related steady state problems which help us obtain the exact longtime behaviors of solution component $(u,v)$. Then we prove there exists the unique classical solution whose longtime behaviors are governed by a spreading-vanishing dichotomy. Lastly, the criteria determining when spreading or vanishing happens are given with respect to the basic reproduction number $\mathcal{R}_0$, the initial habitat $[0,h_0]$, the expanding rates $μ_1$ and $μ_2$ as well as the initial function $(u_0,v_0)$. The criteria reveal the effect of the cooperative behaviors of agents and humans on spreading and vanishing.

math.AP↗

arXiv2021

On monostable cooperative system with nonlocal diffusion and free boundaries

This paper continues to study the monostable cooperative system with nonlocal diffusion and free boundary, which has recently been discussed by [Du and Ni, 2020, arXiv:2010.01244]. We here aim at the four aspects: the first is to give more accurate estimates for solution; the second is to discuss the limitations of solution pair of a semi-wave problem; the third is to investigate the asymptotic behaviors of the corresponding cauchy problem; the last is to study the limiting profiles of solution as one of the expanding rates of free boundary converges to $\yy$. Then two epidemic models are given to illustrate their own longtime behaviors.

math.AP↗

arXiv2013

Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two

In this paper, we study a complete noncompact nonnegatively curved Alexandrov space $A$ with a soul $S$ of codimension two. We establish some structural results under additional regularity assumptions. As an application, we conclude that in this case Sharafutdinov retraction, $π:\ A\to S$, is a submetry.

math.DG↗