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Zhang Shiqing

Publications and source records attributed to Zhang Shiqing.

7 recordsLinked to original sources
arXiv2025

Mathematical Analysis and Modeling of Ebola Virus Dynamics via Optimal Control and Neural Network Paradigms

Ebola virus disease is a severe hemorrhagic fever with rapid transmission through infected fluids and surfaces. We develop a fractional-order model using Caputo derivatives to capture memory effects in disease dynamics. An eight-compartment structure distinguishes symptomatic, asymptomatic, and post-mortem transmission pathways. We prove global well-posedness, derive the basic reproduction number $\mathcal{R}_0$, and establish stability theorems. Sensitivity analysis shows $\mathcal{R}_0$ is most sensitive to transmission rate, incubation period, and deceased infectivity. Treatment-safe burial synergy achieves 86.5\% morbidity-mortality control, with safe burial being most effective. Our disease-informed neural network achieves near-perfect predictive accuracy ($R^2$: 0.991-0.999, 99.1-99.9\% accuracy), closely matching real epidemic behavior.

math.OC↗
arXiv2014

New Periodic Solutions for Second Order Hamiltonian Systems with Local Lipschitz Potentials

Firstly,we generalize the classical Palais-Smale-Cerami condition for $C^1$ functional to the local Lipschitz case,then generalize the famous Benci-Rabinowitz's and Rabinowitz's Saddle Point Theorems with classical Cerami-Palais-Smale condition to the local Lipschitz functional, then we apply these Theorems to study the existence of new periodic solutions for second order Hamiltonian systems with local Lipschitz potentials which are weaker than Rabinowitz's original conditions .The key point of our proof is proving Cerami-Palais-Smale condition for local Lipschitz case,which is difficult since no smooth and symmetry for the potential.

math.FA↗
arXiv2013

Saari's Conjecture and Variational Minimal Solutions for $N$-Body Problems

In this paper, we will prove Saari's conjecture in a particular case by using a arithmetic fact, and then, apply it to prove that for any given positive masses, the variational minimal solutions of the N-body problem in ${\mathbb{R}}^2$ are precisely a relative equilibrium solution whose configuration minimizes the function $IU^2$ in ${\mathbb{R}}^2$.

math-ph↗
arXiv2012

A Simple Method to Construct Local Equilibrium Function for One Dimensional Lattice Boltzmann Method

We have developed a simple method to construct local equilibrium function for one dimensional lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one dimensional Sod flow and one dimensional Lax flow are presented. Favorable results are obtained using proposed new method, indicating that the proposed method is potentially capable of constructing of the local equilibrium function for one dimensional LBM.

math-ph↗
arXiv2012

A New Extension of Serrin's Lower Semicontinuity Theorem

In this paper, we present a new extension of the famous Serrin's lower semicontinuity theorem for the variational functional $\int_Ωf(x,u,u')dx$,we prove its lower semicontinuity in $W_{loc}^{1,1}(Ω)$ with respect to the strong $L_{loc}^{1}$ topology assuming that the integrand $f(x,s,ξ)$ has the usual continuity on all the three variables and the convexity property on the variable $ξ$ and the local absolute continuity on the variable $x$.

math.FA↗
arXiv2012

A New Boundary Scheme for BGK Model

In this paper, we proposed a new boundary condition scheme for the BGK model which has second order accuracy and can be developed to higher accuracy. Numerical tests show that the numerical solutions of the BGK model applied to the new boundary scheme have great agreement with analytical solutions. It is also found that the numerical accuracy of the present schemes is much better than that of the original extrapolation schemes proposed by Guo et al at small grid.

math.NA↗