Applied Mathematics Letters最新文献

In this paper, we study an integrable Camassa–Holm type equation. We proved that if the initial datum $u_0⁄\equiv 0$ is compactly supported in $[a,c]$; then the corresponding solution to the Camassa–Holm type equation has the following property: $u(x,t)=\left(\begin{array}{cc}0,& x>q(c,t);\\ l\left(t\right)e^x,& x<q(a,t).\end{array}\right)$Furthermore, $l\left(t\right)<0$ is a continuous non-vanishing function and strictly decreasing. Long time behavior for the support of momentum density is also studied.

This paper develops a conservative relaxation virtual element method for the nonlinear Schrödinger equation on polygonal meshes. The advantage of this method is to build the virtual element space where the basis functions do not need to be explicitly defined for each local element, and the bilinear forms and nonlinear terms can be computed by using elementwise polynomial projections and pre-defined degrees of freedom. Furthermore, the constructed schemes ensure the conservation of both mass and energy in discrete senses. By using the Brouwer fixed point theorem, we prove the unique solvability of the fully discrete scheme. Finally, some numerical experiments are implemented to verify the theoretical results.

This paper deals with blow-up solutions of a class of initial–boundary value problems for a fourth order parabolic equation involving the Hessian. A lower bound for the lifespan of such solutions is derived.

In this paper, we investigate the uniqueness of periodic wave solutions for a generalized reaction–convection–diffusion equation with arbitrarily high-order reaction term or convection term. The main technique is to prove the monotonicity of the ratio of two Abelian integrals by a new criterion and Descartes’ rule of signs. A positive answer to a conjecture stated in Wei and Chen (2023) is given and some numeric simulations are carried out to illustrate the obtained theoretical results.

In this paper, we consider fast solvers for discrete linear systems generated by Riesz space fractional diffusion equations. We extract a scalar matrix, a compensation matrix, and a $\tau$ matrix from the coefficient matrix, and use their sum to construct a class of $\tau$ splitting iterative methods. Additionally, we design a preconditioner for the conjugate gradient method. Theoretical analyses show that the proposed $\tau$ splitting iterative methods are unconditionally convergent with convergence rates independent of step-sizes. Numerical results are provided to demonstrate the effectiveness of the proposed iterative methods.

In this paper, we consider the numerical method for generalized Allen–Cahn equation with nonlinear mobility and convection term. We propose a linear second-order finite difference scheme which preserves the discrete maximum bound principle (MBP). The scheme is discretized by stabilized Crank–Nicolson in time, upwind scheme for convection term and central-difference scheme for diffusion term. We show that the proposed scheme preserves the discrete MBP under some constraints on temporal step size and stabilizing parameter. Optimal $L^{\infty }$-error estimate is obtained for our scheme. Several numerical experiments are performed to validate our theoretical results.

Based on the local well-posedness for the homogeneous abstract problem, the existence and uniqueness of the local mild and classical solutions have been presented by using Kato’s variable norm technique for the Cauchy problem of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator.

We investigate the Kuramoto model with three oscillators interconnected by an isosceles triangle network. The characteristic of this model is that the coupling connections between the oscillators can be either attractive or repulsive. We list all critical points and investigate their stability. We furthermore present a framework studying convergence towards stable critical points under special coupled strengths. The main tool is the linearization and the monotonicity arguments of oscillator diameter.

Because noise is ubiquitous within-host, a stochastic dynamical system with interval delay is proposed to model the dynamics of HBV infection in vivo. The global existence and nonnegativity of the solutions are established. Virus extinction conditions are derived, under which the asymptotic properties of the virus-free equilibrium are proved, and the persistence conditions are obtained. Finally, numerical simulations are performed to examine the influence of noise on the Hopf bifurcation resulting from the delay parameters in the interval delay.

Decline of immunity is a phenomenon characterized by immunocompromised host and plays a crucial role in the epidemiology of emerging infectious diseases (EIDs) such as COVID-19. In this paper, we propose an age-structured model with vaccination and reinfection of immune individuals. We prove that the disease-free equilibrium of the model undergoes backward and forward transcritical bifurcations at the critical value of the basic reproduction number for different values of parameters. We illustrate the results by numerical computations, and also find that the endemic equilibrium exhibits a saddle–node bifurcation on the extended branch of the forward transcritical bifurcation. These results allow us to understand the interplay between the decline of immunity and EIDs, and are able to provide strategies for mitigating the impact of EIDs on global health.