Published in Acta Mathematica Scientia
We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion, where both fast and slow components are influenced by white noise. Furthermore, we verify the exponential tracking property for the established random slow manifold, which leads to a lower dimensional reduced system. Alongside this we consider a parameter estima...
Published in Acta Mathematica Scientia
In this paper, we consider a delayed diffusive SVEIR model with general incidence. We first establish the threshold dynamics of this model. Using a Nonstandard Finite Difference (NSFD) scheme, we then give the discretization of the continuous model. Applying Lyapunov functions, global stability of the equilibria are established. Numerical simulatio...
Published in Acta Mathematica Scientia
Some sufficient conditions of the energy conservation for weak solutions of incompressible viscoelastic flows are given in this paper. First, for a periodic domain in ℝ3, and the coefficient of viscosity μ = 0, energy conservation is proved for u and F in certain Besov spaces. Furthermore, in the whole space ℝ3, it is shown that the conditions on t...
Published in Acta Mathematica Scientia
This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease. This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al. (An SIR epidemic model with free boundary. Nonlinear Anal RWA, 2013, 14: 1992–2001). We fir...
Published in Acta Mathematica Scientia
By applying the standard fixed point theorems, we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals, supplemented with nonlocal coupled fractional integral boundary conditions. An example is also const...
Published in Acta Mathematica Scientia
In this paper, we construct k-valued random analytic algebroid functions for the first time. By combining the properties of random series, we study the growth and Borel points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.
Published in Acta Mathematica Scientia
The severe acute respiratory syndrome COVID-19 was discovered on December 31, 2019 in China. Subsequently, many COVID-19 cases were reported in many other countries. However, some positive COVID-19 samples had been reported earlier than those officially accepted by health authorities in other countries, such as France and Italy. Thus, it is of grea...
Published in Acta Mathematica Scientia
In this paper, we consider the measure determined by a fractional Ornstein-Uhlenbeck process. For such a measure, we establish an explicit form of the martingale representation theorem and consequently obtain an explicit form of the Logarithmic-Sobolev inequality. To this end, we also present the integration by parts formula for such a measure, whi...
Published in Acta Mathematica Scientia
The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations. In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection (vNR) and the other c...
Published in Acta Mathematica Scientia
In this paper, dynamics analysis of a delayed HIV infection model with CTL immune response and antibody immune response is investigated. The model involves the concentrations of uninfected cells, infected cells, free virus, CTL response cells, and antibody antibody response cells. There are three delays in the model: the intracellular delay, virus ...
