Applied Mathematics Letters最新文献

The conforming discontinuous Galerkin (CDG) method maximizes the utilization of all degrees of freedom of the discontinuous $P_k$ polynomial to achieve a convergence rate two orders higher than its counterpart conforming finite element method employing continuous $P_k$ element. Despite this superiority, there is little theory of the CDG methods for singular perturbation problems. In this paper, superconvergence of the CDG method is studied on a Bakhvalov-type mesh for a singularly perturbed reaction–diffusion problem. For this goal, a pre-existing least squares method has been utilized to ensure better approximation properties of the projection. On the basis of that, we derive superconvergence results for the CDG finite element solution in the energy norm and $L^2$-norm and obtain uniform convergence of the CDG method for the first time.

In this paper, a semi-discrete matrix coupled dispersionless system is presented. A Lax pair is proposed, and the Darboux transformation is employed to construct exact solutions to the semi-discrete matrix coupled dispersionless system. These solutions numerically exhibit a variety of exact phenomena, including periodic patterns, breathers, rogue waves, and bright and dark solitons.

The aim of this paper is to justify the rigorous derivation of the incompressible Navier–Stokes equations from the nonlinear Vlasov–Fokker–Planck (VFP) equation with a constant temperature. Under the incompressible Navier–Stokes scaling, we first establish the global existence of regular solutions to the rescaled nonlinear VFP equation near the Maxwellian, obtaining some uniform bound estimates. We then show the strong convergence of solution to the nonlinear VFP equation towards the incompressible Navier–Stokes system.

In this paper, we develop a new space-fractional modified phase field crystal equation which has some similar properties including the mass conservation and energy dissipation. Then, we propose a second-order scheme based on a new Lagrange multiplier method that conserves the mass and dissipates the energy. For the new method, there are only two decoupled linear equations with constant coefficients and one nonlinear algebraic system to be solved at each time step which makes it efficient. Finally, we give some numerical experiments to verify the accuracy and stability of the proposed methods.

In this paper, we investigate a cytokine-enhanced model of virus infection. This model of viral infection was also characterized by impaired immune function or immunosuppression. By analyzing this model, we can determine the effect of inflammatory cytokines on it. When control of inflammatory cytokines is lost, the elite control threshold $n^{\ast \ast }$ increases, making it more difficult to control the virus. Under certain conditions, the model exhibits saddle–node bifurcation and forward/backward bifurcation. We consider the robustness of the system as the difficulty of the virus to rebound. When inflammatory cytokines are out of control, the virus is more likely to rebound.

We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson. Through the prism of the quest to quantise gravitational waves in curved spacetimes, we study their properties from the point of view of ellipticity, gauge invariance, and the existence of a spectral gap.

In this paper, we study global asymptotic stability of all equilibria of a virus dynamic model with general monotonic incidence, two time delays, CTL and antibody immune responses by constructing Lyapunov functionals and applying LaSalle’s invariance principle.

We prove the stability of the magnetic Bénard system with partial dissipation on perturbations near a background magnetic field in $T^2$. Neglecting the effect of the temperature, the stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit large-time decay rate of the solutions.

We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis in the fast switching regime shows that the total cell density in the two-population go-or-grow model can be described in terms of a single reaction–diffusion equation with density-dependent diffusion and proliferation. Using the connection to single-population models, we study travelling wave solutions, showing that the wave speed in the go-or-grow model is always bounded by the wave speed corresponding to the well-known Fisher–KPP equation.

In this paper, the nonlinear wave solutions for Gross–Pitaevskii equation on the periodic wave background are investigated by Darboux-Bäcklund transformation, from which the soliton and breather wave solutions on the Jacobi elliptic cn and dn functions backgrounds are derived. The corresponding evolutions and dynamical properties of nonlinear wave solutions under different parameters are discussed. These results reported in this paper may raise the possibility of related experiments and potential applications in nonlinear science fields, such as nonlinear optics, oceanography and so on.