We prove that the asymptotic behavior of the Stratonovich counterpart of the Itô’s type stochastic SIR model investigated in Tornatore et al. (2005), Ji and Jiang (2012, 2014) is ruled by the same threshold as the deterministic system. In other words, in contrast to the Itô’s model, the intensity of the noise described through the Stratonovich calculus is not relevant for the extinction of the disease

In this paper, we revisit the commensalism model proposed and analyzed recently by Jawad (2022). By applying the standard comparison theorem and the theory of asymptotically autonomous systems, we completely describe the partial survival, permanence, and global stability of the positive equilibrium of the system. These results not only complement but also essentially improve the corresponding ones

A novel systematical solution procedure of the (2+1)-dimensional Konopelchenko-Dubrovsky equation is employed on the basis of the ∂̄-dressing method. The eigenfunctions and Green’s function of the Lax pair play a fairly important role in constructing the scattering equation. By analyzing the analyticity of the eigenfunctions and Green’s function, a new ∂̄ problem is introduced to help explore the solution

The linear self-interacting diffusion driven by fractional Brownian motion is approximated by an explicit numerical scheme in this paper. The present method’s mean-square convergence is investigated, and the order of convergence is established to be 1. To demonstrate the performance of the suggested method, a numerical simulation is performed.

In the present paper, we study an inhomogeneous pseudo-parabolic equation with nonlocal nonlinearity ut−kΔut−Δu=I0+γ(|u|p)+ω(x),(t,x)∈(0,∞)×RN,where p>1,k≥0, ω(x)≠0 and I0+γ is the left Riemann–Liouville fractional integral of order γ∈(0,1). Based on the test function method, we have proved the blow-up result for the critical case γ=0,p=pc for N≥3, which answers an open question posed by Zhou (2020)

In this paper, we consider low rank matrix recovery with impulsive noise. We first study the difference of nuclear norm and Frobenius norm model and present a stable recovery result based on the matrix restricted isometry property. Then we find the truncated difference of nuclear norm and Frobenius norm model can also stably recover low rank matrices with impulsive noise.

This letter investigates the temporally localized lumps on a background of two-dimensional (2D) homoclinic orbits in the Fokas system. These special lumps are localized in time as well as in 2D space and have completely different dynamical behaviours compared with usual lumps, and they are called “rogue lumps”. It is shown that these rogue lumps first arise from homoclinic orbits, and then remain propagating

Based on generalized Lax equations and the Sato theory on KP and mKP hierarchies derived from the basic algebra of pseudo-differential operators, Miura- and auto-Bäcklund transformations can be derived from the gauge transformations of the Lax operators. In this paper, we study the gauge transformations of two-component KP and mKP hierarchies using the two-component generalized gauge transformations

The presence of sharp minima in nondifferentiable optimization models has been exploited, in the last decades, in the benefit of various subgradient or proximal methods. One of the long-lasting general proximal schemes of choice used to minimize nonsmooth functions is the Proximal Point Algorithm (PPA). Regarding the basic PPA, several well-known works proved finite convergence towards weak sharp minima

We are concerned here with results of existence and regularity of solutions to a stationary MHD problem, with a possibly multi-connected 2D domain associated with Navier-type boundary conditions. The RHS f, corresponding to the external forces, is in Lp(Ω), with p≥2, without any restriction on its norm. Two main difficulties are encountered in solving these problems: the geometry of the domain and

Due to short test time, heat conduction was considered as transient in hypersonic shock tunnels. The heat flux measurement and data processing were operated basing on one-dimensional semi-infinite heat conduction theory. However, for models with local large curvature or small radius, it resulted in significant compression or expansion of space for heat transfer, or lateral heat conduction, which made

In this paper, we are concerned with the diffusive SIR and SEIR epidemic models with multiple parallel infectious stages and nonlinear incidence mechanism. We first establish a priori L∞-norm estimates for the solutions to the epidemic models, and then derive the global attractivity of disease-free equilibrium and endemic equilibrium for the two models in terms of the basic reproduction number. Our

In this work, for the two dimensional anisotropic diffusion problem, the classical kth order finite element solution is postprocessed to obtain a new finite volume element solution, such that the new solution satisfies the local conservation property on a certain dual mesh, and converges to the analytic solution with optimal rates. The postprocessing algorithm has a local nature and can be conducted

An extended lattice Boltzmann model is proposed for the anisotropic solidification process based on the quantitative phase-field equation. To include the anisotropy, we derive an equivalent diffusion matrix and design an off-diagonal relaxation-time matrix to recover it within the framework of the lattice Boltzmann method. Different from the standard collision-streaming algorithm, a correction step

Under investigation in this work is the Degasperis–Procesi equation with a strong dispersive term, which can be investigated as a model for shallow water dynamics. With the help of distribution theory, a direct and effective way is used to succinctly study the multi-peakon solutions of the equation. These multi-peakon solutions are obtained in weak sense. In particular, several types of double-peakon

In recent paper, we will consider some properties of weak solutions to the Dirichlet problem of a system with cubic nonlinearities from biaxial nematic liquid crystals in two dimensions. The smoothness of weak solution is obtained firstly. Then we study the constant boundary value problems of this system and obtain a Liouville-type theorem.

In this note we provide an algorithm for computing the fractional integrals of orthogonal polynomials, which is more stable than the one based on the expansion of the polynomials w.r.t. the canonical basis. This algorithm is aimed at solving corresponding fractional differential equations. A few numerical illustrations are reported.

Under investigation in this paper is a higher order wave equation of the Korteweg–de Vries type, which describes the propagation of more complex wave in the shallow water. Bilinear form is derived based on the binary Bell polynomials. One-soliton solutions are constructed via the Hirota method. Two-soliton solutions are tried to be constructed, but it degenerates to the one-soliton solutions. Influences

A new kind of modulus-based matrix splitting methods is proposed to solve the vertical linear complementarity problems in a direct way. This kind of methods is different from the existing modulus-based formulation which based on an equivalent form of the problem. Convergence of the new methods is proved under certain conditions. Numerical experiments are given to show that the efficiency of the new

In this note, we consider a multi-strain cholera model with an imperfect vaccine. First, the existence and uniqueness of the endemic equilibrium of the model is proved. In addition, by constructing suitable Lyapunov function and using LaSalle’s invariance principle, it is proven that the endemic equilibrium of the model is globally asymptotically stable in a special case. This partially verifies the

In unbounded domain RN,N≥1, we consider the defocusing nonlinear Schrödinger equation with power-type nonlinearity containing −|u|4N−2su. For 2s∗=2N−2s, with s

In this paper, we establish a new result on the existence of the radial solutions for an eigenvalue problem of singular augmented Hessian equation. By adopting some suitable growth conditions and combining the method of upper and lower solutions, we derive a sufficient condition for the existence of radial solutions of the equations in which the nonlinearity may be singular in some space variables

This paper is concerned with the numerical simulations for the dynamics of the time-fractional molecular beam epitaxy models. The variable-step Crank–Nicolson-type schemes are proposed and analyzed for model with and without slope selection respectively. By using the discrete gradient structures of discrete fractional derivative, the numerical schemes preserve discrete variational energy dissipation

In this paper, a series of generalized-formed equations describing the fluid flow, combined with the heat and mass transfer of viscoelastic fluid under the impacts of Dufour and Soret effects are presented. The constitutive relation of viscoelastic fluid, modified Fick’s model and Fourier’s law are all considered as fractional types. Assume that the ultrafiltration process happens in a funnel, and

In this paper, we establish an influenza A epidemic model with vaccination and asymptomatic patient. The most important is that the method of the stability proof at the endemic equilibrium. We convert the model to a nonlinear Volterra integral equation, and prove the stability at the origin of this integral equation to obtain the local stability of the endemic equilibrium. Furthermore, combining with

In this paper we use the constrained mock-Chebyshev least squares interpolation to obtain stable quadrature formulas with high degree of exactness and accuracy from equispaced nodes. We numerically prove the effectiveness of the proposed algorithm by several examples.

In this paper, the combination of Painlevé analysis and Lie group method is performed, the Painlevé properties (PPs) and Bäcklund transformations (BTs) of the nonlinear ϕ4 types of equations are obtained under some conditions. Then, all of the point symmetries of the generalized ϕ4 model are given by Lie group classification method. Furthermore, the exact solutions to the equations are investigated

In this paper, we propose a procedure that can be added to any iterative scheme in order to turn it into an iterative method for approximating all roots simultaneously of any nonlinear equations. By applying this procedure to any iterative method of order p, we obtain a new scheme of order of convergence 2p. Some numerical tests allow us to confirm the theoretical results and to compare the proposed

For the diffusive Nicholson’s Blowflies equation accompanying disparate mature delay and feedback delay, the traveling wave front analysis has not been touched. By using the inequality technique and constructing suitable upper and lower solutions, we successfully built up a novel criterion to ensure the existence of traveling wave front solutions of the proposed model, which is essentially new and

In this letter, to fit the character of solutions to impulsive boundary value problems (IBVPs), we firstly construct a piecewise continuous space using the reproducing kernel function (RKF) of smooth reproducing kernel Hilbert space (RKHS) W3. Then we present a fourth order convergent collocation approach for IBVPs by using the piecewise continuous basis functions yielded by RKFs in W3. Also, the convergence

Cage culture, as a kind of aquaculture, is increasingly becoming the main way to provide aquatic products due to its merits of high output and easy management. However, the main issue for the fishermen to be concerned about is the determination of the reasonable amount of casting bait since excess feeding bait will not only deteriorate water quality but also increase farming costs while too little

Wave breaking (bounded solutions with unbounded derivative) of the hyperbolic equation is important and interesting to physicist and mathematician. In this article, thanks to the conservation law, we derive some new wave breakings of a class of strong solutions for a 3-component Camassa–Holm equation.

In this paper, we study the following nonlinear Dirac equation (NDE)−i∑k=13αk∂ku+mβu=K(x)|u|p−2u+λu,where u:R3→ℂ4, K∈L∞(R3), m>0 is the mass of the electron, λ∈(−m,m) is an unknown parameter, ħ is Planck’s constant, ∂k=∂∂xk, α1,α2,α3, β are 4 × 4 Pauli–Dirac matrices and p∈(2,83). We present a new approach which is based on some prior estimates, and show that the spectrum point m is a bifurcation point

In this paper, we consider the new version of the Turing model proposed by Kondo (2017), which is called the kernel-based Turing model. The main aim is to study the sharp changes of interaction between local and nonlocal on the solutions of Turing model. Our results reveal that the kernel (or nonlocal) makes a key effect on the long time behavior of evolution equation, where the stable patterns appear

Alzheimer’s disease (AD) is a neurodegenerative disorder with multifactorial etiology that poses a serious threat to human health. This work is devoted to a stochastic reaction–diffusion system for AD with space–time white noise accounting, which describes the positive feedback loop among the Aβ and the Ca2＋. The existence and uniqueness of mild solutions for the system are obtained by using the truncation

In this paper, a new version of the solution in form of Grammian for the (2+1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili equation is obtained with the aid of the polynomial function. A family of multiple lump solutions are constructed. All the center points of the lumps form a triangular structure as the auxiliary variable tends to the negative or positive large values. A unified scheme for

This work develops the boundary knot method (BKM) for two-dimensional (2D) coupled thermoelasticity problems in the frequency domain. By taking the non-singular general solution satisfying the governing equations as the basis function, the BKM does not require domain discretization. Nevertheless, the non-singular solution for the considered problems is absent. The Helmholtz decomposition and eigen-analysis

In this article we study the existence of solutions of a system of partial differential equations of elliptic type, describing the distribution of a biological species “u” and the density of a chemical stimulus “ψ” in a bounded domain Ω of RN. The equation for u includes a chemotaxis term with nonlinear flux limitation which depends on the exponent p>1. The equation for u is given by −div(M(x)∇u)+

Dynamics of predator–prey systems is of great importance in ecosystems. In this paper, we present and analyse a stochastic eco-epidemiological predator–prey model where the influence of anti-predator behaviour is investigated due to the fear induced from the predators. Through mathematical analysis, it has been observed that the model has a unique and global positive solution. Sufficient criteria are

The distributed-order model is equivalent to weighting the fractional-order model on a given interval. In this paper, a double time-distributed order Maxwell model is developed and formulated to study the characteristics of a start-up pipe flow. The numerical solution of the distributed-order governing equation is obtained by the finite difference method. In order to test the convergence of numerical

In this paper, we propose an age-structured SVIRS model with two loss routes of immunity. Employing the Lyapunov–Schmidt approach, we derive a necessary and sufficient condition for the occurrence of a backward bifurcation. We identify that the combined action of such two losses of immunity plays a vital role in producing a bistable phenomena.

This paper is concerned to the class of generalized quasilinear Schrödinger equations which have appeared from plasma physics, as well as high-power ultrashort laser in matter. By introducing a variable replacement and using some iterative methods, the existence and nonexistence of entire large solutions are studied.

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis shows that the proposed method converges under the randomized row selection rule and the convergence rate in expectation is also addressed. Numerical experiments further demonstrate that the proposed algorithms are

This paper analyzes the convergence of the fast L1 method for the semi-linear time-factional subdiffusion equations. The tool we use is the generalized discrete Gronwall inequality. We show that the difference between the solution of the L1 method and the solution of the fast L1 method can be arbitrarily small and is independent of the sizes of the time and/or space grids. Our proof is very simple

We are concerned with the optimal decay rates for higher-order spatial derivatives of strong solutions to the 3D Cauchy problem of the magneto-micropolar fluid equations. Under some smallness assumptions, it is shown that for any integer N≥3, the N−1-order and N-order spatial derivatives of the solutions converge to zero at the L2-rate (1+t)−(34+N−12) and (1+t)−(34+N2) respectively, which are the same

In this paper, we assumed that the parameter in the SVEIS epidemic model satisfies the mean-reverting Ornstein–Uhlenbeck process, and propose a new stochastic SVEIS model. Through constructing suitable Lyapunov function, we prove that this stochastic model has a stationary distribution when the critical value R0s>1. Then the sufficient condition R0e<1 for the exponential extinction is also established

We consider an inverse eigenvalue problem for constructing an n×n Jacobi matrix Jn under the circumstance that its all eigenvalues, except for one and a part of the matrix Jn are given. To be precise, the known partial data of Jn means either its leading principal submatrix J[(n+1)/2] when n is odd, or the submatrix J[(n+1)/2] together with the [(n+1)/2]×(n/2+1) codiagonal element when n is even. The

In this letter, we propose a new semi-discrete complex coupled system associated with 4 × 4 Lax pair. Firstly, the continuous limit technique is used to map this semi-discrete system to two new continuous complex equations. Then, the discrete generalized (m,N−m)-fold Darboux transformation for this system is first proposed. Finally, through applying the resulting Darboux transformation, some novel

By using the Mawhin’s continuation theorem, this paper establishes a criterion for the existence of periodic orbits of the planar differential systems with delay angle. An example is provided to illustrate the application of the result.

In this paper, the best approximate solution of Fredholm integral equations of the first kind with some scattered observations is studied. An explicit approximate solution has been obtained by our proposed method and converges to the exact solution with minimum norm of the integral equations with probability 1, which is identical with the solution by means of the regularization method. In addition

In this Letter, we investigate an extended (3+1)-dimensional nonlinear Schrödinger equation in an optical fiber. Via the truncated Laurent expansions, auto-Bäcklund transformations are obtained. According to the Ablowitz-Kaup-Newell-Segur procedure, we derive a Lax pair under certain optical-fiber coefficient constraints. Via the Hirota method, we obtain some bilinear forms, bright two-soliton and

We prove a Liouville theorem on the positive bounded entire solution of a class of reaction–diffusion systems with fractional diffusion. Some application of this Liouville theorem is also given.

The coupled Burgers’ equations at high Reynolds numbers usually have sharp gradients or are discontinuous in the solution. Therefore, it is difficult to obtain analytical solutions. This paper aims to use the moving finite element method proposed by Li et al. (2001) to get stable and high-precision numerical solutions for the coupled Burgers’ equations at high Reynolds numbers. The method decouples

Seismic wave equations based on numerical simulation have become effective tools in geological exploration. Considering the frequency dependence of reflections and fluid saturation in porous mediums, the diffusive–viscous wave theory is necessary to study. In this paper, a cell-centered finite volume scheme for the diffusive–viscous wave equation is proposed on general distorted polygonal meshes. Numerical

In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary diffe- rential equations numerically. The advantage of the LMM-RE approach is that the combined method possesses higher order and favorable linear stability properties

In this paper, we propose an efficient numerical algorithm for reaction–diffusion equation on the general curved surface. The surface is discretized by a mesh consisting of triangular grids. The partial differential operators are defined based on the surface mesh and its dual surface polygonal tessellation. The proposed method has three advantages including intrinsic geometry, conservation law, and

Recently, the existence and uniqueness of positive solution for multilinear systems with H+-tensor were proved by Wang et al. (2019). To expand the range of multilinear systems with positive solutions, a new class of tensors, called generalized strong M-tensor, is proposed while the H+-tensor is a special case of the generalized strong M-tensor. Under certain conditions, the existence and the uniqueness

In this note we show that, under certain conditions on the coefficients, the solutions of the parabolic phase-lag heat conduction models are determined by an analytic semigroup for which the inner product determines the H2-norm of the temperature. As a consequence the H2-norm of the temperature decays in an exponential way.

Our primary objective of this article is to study a class of nonlinear telegraph systems. Some new criteria for the existence and multiplicity of positive doubly periodic solutions are established. Many positive doubly periodic solutions are also considered.

Positive-definite kernels are probably best known for their application in many problems driven by scattered data interpolation. Fasshauer and Ye introduced constructive theory of reproducing kernels of generalized Sobolev spaces in 2011 to provide insight into the types of functions being well approximated by these kernels on a set of scattered points. In this approach, the reproducing kernel is viewed