Searcharxiv⌕ Search

arXiv subjects

Mingxin Wang

Publications and source records attributed to Mingxin Wang.

At least 55 records · Page 3Linked to original sources
arXiv2021

A 500 MS/s waveform digitizer for PandaX dark matter experiments

Waveform digitizers are key readout instruments in particle physics experiments. In this paper, we present a waveform digitizer for the PandaX dark matter experiments. It supports both external-trigger readout and triggerless readout, accommodating the needs of low rate full-waveform readout and channel-independent low threshold acquisition, respectively. This digitizer is a 8-channel VME board with a sampling rate of 500 MS/s and 14-bit resolution for each channel. A digitizer system consisting of 72 channels has been tested in situ of the PandaX-4T experiment. We report the system performance with real data.

physics.ins-det↗
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↗
arXiv2021

Free boundary problems of a mutualist model with nonlocal diffusions

A mutualist model with nonlocal diffusions and a free boundary is first considered. We prove that this problem has a unique solution defined $t\ge0$, and its dynamics are governed by a spreading-vanishing dichotomy. Some criteria for spreading and vanishing are also given. Of particular importance is that we find that the solution of this problem has quite rich longtime behaviors, which vary with the conditions satisfied by kernel functions and are much different from those of the counterpart with local diffusion and free boundary. At last, we extend these results to the model with nonlocal diffusions and double free boundarie

math.AP↗
arXiv2021

Sharp estimates for a nonlocal diffusion problem with a free boundary

In this paper, we proceed to study the nonlocal diffusion problem proposed by Li and Wang [8], where the left boundary is fixed, while the right boundary is a nonlocal free boundary. We first give some accurate estimates on the longtime behavior by constructing lower solutions, and then investigate the limiting profiles of this problem when the expanding coefficient of free boundary converges to $0$ and $\yy$, respectively. At last, we focus on two important kinds of kernel functions, one of which is compactly supported and the other behaves like $|x|^{-γ}$ with $γ\in(1,2]$ near infinity. With the help of some upper and lower solutions, we obtain some sharp estimates on the longtime behavior and rate of accelerated spreading.

math.AP↗
arXiv2021

Global solvability of a predator-prey model with predator-taxis and prey-taxis

This paper is concerned with a diffusive predator-prey model with predator-taxis and prey-taxis. Based on the Schauder fixed point theorem, we prove the global existence, uniqueness and boundedness of the classical solutions under the conditions that the predator-taxis and prey-taxis effects are weak enough.

math.AP↗
arXiv2021

Dynamics for nonlocal diffusion problems with a free boundary and a fixed boundary

In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain the global existence, uniqueness and longtime behaviour of solution of these two problems. The spreading-vanishing dichotomy and sharp criteria for spreading and vanishing are established. We also prove that accelerated spreading could happen if and only if a threshold condition is violated by kernel function. Then we discuss a classical Lotka-Volterra predator-prey model with nonlocal diffusions and a free boundary which can be seen as nonlocal diffusion counterpart of the model in the work of Wang (2014 J. Differential Equations \textbf{256}, 3365-3394).

math.AP↗
arXiv2020

Positive Solutions of Competition Model with Saturation

In this paper, the positive solutions of a diffusive competition model with saturation are mainly discussed. Under certain conditions, the stability and multiplicities of coexistence states are analyzed. And by using the topological degree theory in cones, it is proved that the problem has at least two positive solutions under certain conditions. Finally, investigating the bifurcation of coexistence states emanating from the semi-trivial solutions, some instability and multiplicity results of coexistence state are expressed.

math.AP↗
arXiv2020

Global stability of spatially nonhomogeneous steady state solution in a diffusive Holling-Tanner predator-prey model

The global stability of the nonhomogeneous positive steady state solution to a diffusive Holling-Tanner predator-prey model in a heterogeneous environment is proved by using a newly constructed Lyapunov function and estimates of nonconstant steady state solutions. The techniques developed here can be adapted for other spatially heterogeneous consumer-resource models.

math.AP↗
arXiv2020

A viral propagation model with nonlinear infection rate and free boundaries

In this paper we put forward a viral propagation model with nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential equation, in which the spatial range of the first equation is the whole space $\mathbb{R}$, and the last two equations have free boundaries. As a new mathematical model, we prove the existence, uniqueness and uniform estimates of global solution, and provide the criteria for spreading and vanishing, and long time behavior of the solution components $u,v,w$. Comparing with the corresponding ordinary differential systems, the {\it Basic Reproduction Number} ${\cal R}_0$ plays a different role. We find that when ${\cal R}_0\le 1$, the virus cannot spread successfully; when ${\cal R}_0>1$, the successful spread of virus depends on the initial value and varying parameters.

math.AP↗
arXiv2019

Free boundary problems with nonlocal and local diffusions I: Global solution

We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the population dispersal, with the free boundary representing the spreading front of the species. We prove that such kind of nonlocal and local diffusion problems has a unique global solution, and then show that a spreading-vanishing dichotomy holds. Moreover, criteria of spreading and vanishing, and long time behavior of solution when spreading happens are established for the classical Lotka-Volterra competition and prey-predator models. Compared with free boundary systems with local diffusions as well as with nonlocal diffusions, the present paper involves some new difficulties, which should be overcome by use of new techniques. This is part I of a two part series, where we prove the existence, uniqueness, regularity and estimates of global solution. The spreading-vanishing dichotomy, criteria of spreading and vanishing, and long-time behavior of solution when spreading happens will be studied in the separate part II.

math.AP↗
arXiv2019

Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka-Volterra competition model

A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which the diffusion coefficients, resource functions and competition rates are all spatially heterogeneous, the positive equilibrium solution is globally asymptotically stable when it exists. Secondly the existence and global asymptotic stability of the positive and semi-trivial equilibrium solutions are obtained for the model with arbitrary number of species under the assumption of spatially heterogeneous resource distribution. A new Lyapunov functional method is developed to prove the global stability of a non-constant equilibrium solution in heterogeneous environment.

math.AP↗
arXiv2019

Two species nonlocal diffusion systems with free boundaries

We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the species, but here the population dispersal is described by "nonlocal diffusion" instead of "local diffusion". We prove that such a nonlocal diffusion problem with free boundary has a unique global solution, and for models with Lotka-Volterra type competition or predator-prey growth terms, we show that a spreading-vanishing dichotomy holds, and obtain criteria for spreading and vanishing; moreover, for the weak competition case and for the weak predation case, we can determine the long-time asymptotic limit of the solution when spreading happens. Compared with the single species free boundary model with nonlocal diffusion considered recently in \cite{CDLL}, and the two species cases with local diffusion extensively studied in the literature, the situation considered in this paper involves several extra difficulties, which are overcome by the use of some new techniques.

math.AP↗
arXiv2017

Dynamics for the diffusive Leslie-Gower model with double free boundaries

In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the free boundaries represent expanding fronts of the predator species. We first prove the existence, uniqueness and regularity of global solution. Then provide a spreading-vanishing dichotomy, namely the predator species either successfully spreads to infinity as $t\to\infty$ at both fronts and survives in the new environment, or it spreads within a bounded area and dies out in the long run. The long time behavior of $(u,v)$ and criteria for spreading and vanishing are also obtained. Because the term $v/u$ (which appears in the second equation) may be unbounded when $u$ nears zero, it will bring some difficulties for our study.

math.AP↗
arXiv2017

Dynamics for a diffusive prey-predator model with different free boundaries

To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect each other as time evolves, are used to describe the spreading of prey and predator. We investigate the existence and uniqueness, regularity and uniform estimates, and long time behaviors of global solution. Some sufficient conditions for spreading and vanishing are established. When spreading occurs, we provide the more accurate limits of (u,v) as t\to\infty, and give some estimates of asymptotic spreading speeds of u,v and asymptotic speeds of g,h. Some realistic and significant spreading phenomena are found.

math.AP↗