Narrow Results

In this paper, we propose a stochastic cholera model that incorporates media coverage and two time delays driven by Lévy noise in order to deeply understand the propagation process of cholera in the real world, generalized nonlinear incidence rates ${\beta }_1(M)$ and ${\beta }_2(M)$ are also introduced. First, we discuss the existence and uniqueness of the global positive solution of the stochastic model by using the Lyapunov method. Moreover, the dynamic properties of stochastic solution around the disease-free and endemic equilibria are demonstrated. At last, we present numerical simulation results to reveal how Lévy jumps, time delays and media coverage affect the asymptotic properties of the stochastic model.

In this paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system:

In this paper, we investigate the Cauchy problem for Cahn–Hilliard equation with inertial term in n-dimensional space. Based on the decay estimate of solutions to the corresponding linear equation, we define a solution space. Under small condition on the initial value, we prove the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces by the contraction mapping principle.

In this paper, we study the asymptotic behavior of Palais-Smale sequences associated with the prescribed mean curvature equation on a compact manifold with boundary. We prove that every such sequence converges to a solution of the associated equation plus finitely many “bubbles” obtained by rescaling fundamental solutions of the corresponding Euclidean boundary value problem.

Let ${\lambda }_f(n)$ and ${\lambda }_g(n)$ be the normalized $n^{\mathrm{\text{th}}}$-Fourier coefficient of distinct Hecke eigenforms $f$ and $g$ of integral weight for the full modular group, respectively, and $Q(\underline{x})$ is a primitive integral positive-definite binary quadratic form of fixed discriminant $D<0$ with the class number $h(D)=1$. We establish a lower bound for the analytic density of the set

In this paper, we consider a fully parabolic attraction-repulsion chemotaxis model with logistic source. First of all, we obtain an explicit formula ${\mu }_0$ for the logistic damping rate $\mu$ such that the model has no blow-up when $\mu >{\mu }_0$. In addition, the asymptotic behavior of the solutions is studied. Our results partially generalize and improve some results in the literature, and partially results are new.

This paper centers its attention on an anisotropic area-preserving flow with the goal of establishing the existence of smooth solutions to the even, planar logarithmic Minkowski problem by the asymptotic behavior of this flow.

In this work, we have studied the late-time behavior of initially expanding homogeneous cosmological models with a positive cosmological term in Randall–Sundrum brane-world type scenarios. The matter fields are confined in the three-brane, onto which the five-dimensional Weyl tensor has a nonvanishing projection. It is found that all Bianchi models (except IX) exponentially evolve toward the de Sitter solution while the Bianchi IX model also isotropizes but with a restriction on the cosmological parameter.

High energy elastic pp scattering at the Large Hadron Collider (LHC) at c.m. energy 14 TeV is predicted using the asymptotic behavior of σ_tot(s) and ρ(s) known from dispersion relation calculations and the measured elastic differential cross-section at . The effective field theory model underlying the phenomenological analysis describes the nucleon as having an outer cloud of quark–antiquark condensed ground state, an inner core of topological baryonic charge of radius ≃ 0.44 F and a still smaller valence quark-bag of radius ≲ 0.1 F. The LHC experiment TOTEM (Total and Elastic Measurement), if carried out with sufficient precision from |t| = 0 to |t| > 10 GeV², will be able to test this structure of the nucleon.

In this paper, we calculate the vacuum energy as a functional from the phion propagator in 4D model of complex scalar field (phion) which interacts with a real matrix scalar field (chion). The condition of stationarity of this functional gives us the equation for phion propagator. At some critical value of the coupling, the propagator changes its asymptotic behavior in the deep-Euclidean region of momenta. This behavior corresponds to some critical phenomenon. The study of the convexity of the energy functional shows that the solution obtained actually corresponds to the theory. We also discuss the stabilization of the ground state in the strong-coupling region by effective self-action of phions.

This study extracts heat transfer analysis for the axisymmetric flow of CuO-water nanofluid imposing normal to a spiraling disk uniformly rotating and radially stretching. The combined influence of uniformly rotating and linearly radial stretching surface engenders the logarithmic spirals in motion. The governing system is transformed into a system of the ordinary differential equations that represent the flow. The Tiwari–Das [Int. J. Heat Mass Trans. 50, 2002 (2007)] model is utilized to envisage the heat transfer and other physical properties of the nanofluid. A highly precise numerical technique named as Legendre wavelet-based spectral method is practiced to computing the impacts of the pertinent variables on the flow. The results of physical significance including the wall shear, skin frictions and heat transfer rate are attained for the multiple spiraling parameters and the nanoparticle volume fraction. The asymptotic results for the large spiraling parameter are also presented to analyze the flow behavior for the high spiraling parameter. The influence of the nanoparticles is also investigated and the enhancement in thermal conductivity is measured. The temperature and thermal layer thickness reduce for large spiraling parameter. Also addition of the nanoparticles enhances the heat transfer rate of the nanofluid.

Under investigation in this paper is a two-component Novikov system (also called Geng-Xue equation), which was proposed by Geng and Xue in 2009. Firstly, via the Lie symmetry method, infinitesimal generators, commutator table of Lie algebra and symmetry groups of the two-component Novikov system are presented. At the same time, some group invariant solutions are computed through similarity reductions. In particular, we construct peakon solution by applying the distribution theory. In addition, based on obtained group invariant solutions and symmetry transformations, we derive some new exact solutions, which include stationary solutions, smooth solutions, and a weak solution. The analytical properties to some of group invariant solutions and new exact solutions are discussed, such as decay, asymptotic behavior, and boundedness.

This study focuses on the asymptotic properties of quenching solutions for the quasilinear parabolic electrostatic micro-electro-mechanical system with singular logarithm boundary flux. Under some assumptions on initial data, quenching in finite time, blowup phenomenon of a time derivative, lower and upper bounds of quenching rate are studied theoretically, and the asymptotic behaviors near quenching time are verified numerically.

In this paper we study the relationship between the asymptotic behavior of a numerical simulation by linear multistep method and that of the true solution itself for fixed step sizes. The numerical method is viewed as a dynamical system in which the step size acts as a parameter. Numerical stability of linear multistep method for nonlinear delay differential equation is investigated and we prove that A-stable linear multistep methods are NP-stable. It is shown that a consistent zero-stable linear multistep method does not admit spurious fixed points. The existence of spurious period-two solutions in the time-step is also studied. Finally we give a simple example to illustrate instability of the spurious period-two solutions.

A nonlinear recurrence involving a piecewise constant McCulloch–Pitts function and two 2-periodic coefficient sequences is investigated. By allowing the threshold parameter to vary from 0⁺ to +∞, we work out a complete bifurcation analysis for the asymptotic behaviors of the corresponding solutions. We show that there are four steady state solutions and that all solutions will tend to one of them. We hope that our results will be useful in further investigating neural networks involving the McCulloch–Pitts function with threshold and more general periodic coefficients.

The main aim of this paper is to analyze the asymptotic behavior of a nonautonomous integro-differential parabolic equation of diffusion type with a memory term, expressed by convolution integrals involving infinite delays, in an unbounded domain. The assumptions imposed do not ensure uniqueness of solutions of the corresponding initial value problems. The theory of set-valued nonautonomous dynamical systems is applied to prove the existence of pullback attractors for our model. To do this, we first analyze an abstract version of the equation.

In this paper, we are concerned with the wave propagation for a system of 2-D lattice differential equations with delay. Under the monostable assumption, the asymptotic behavior, the monotonicity and uniqueness of traveling wave are established when the wave speed is greater than or equal to the minimal wave speed c_*(θ) > 0. In addition, the directional dependence of the minimal wave speed is analyzed numerically.

In this paper, a diffusive activator–inhibitor model in vascular mesenchymal cells is considered. On one hand, we investigate the stability of the equilibria of the system without diffusion. On the other hand, for the unique positive equilibrium of the system with diffusion the conditions ensuring stability, existence of Hopf and steady state bifurcations are given. By applying the center manifold and normal form theory, the normal forms corresponding to Hopf bifurcation and steady state bifurcation are derived explicitly. Numerical simulations are employed to illustrate where the spatially homogeneous and nonhomogeneous periodic solutions and the steady states can emerge. The numerical results verify the obtained theoretical conclusions.

In this paper, we study the steady-state problem of an S-K-T competition model with a spatially degenerate intraspecific competition coefficient. First, the global bifurcation continuum of positive steady-state solutions from its semitrivial steady-state solution is given, which depends on the spatial heterogeneity and cross-diffusion. Second, two limiting systems are derived as the cross-diffusion coefficient tends to infinity. Moreover, we demonstrate the existence of positive steady-state solutions near the two limiting systems, and show which one of the limiting systems characterizes the positive steady-state solution.

We study the asymptotic behavior of the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter ε > 0. We give an explicit form of the singular part of the corresponding potential u^ε which allows to construct the limit potential u (as ε → 0) and an approximation of the inductance coefficient L^ε. We establish some estimates of the deviation u^ε - u and of the error of approximation of the inductance. We show that L^ε behaves asymptotically as ln ε, when ε → 0.