A multi-agent wealth exchange model, which considers a varying trading propensity and a control of wealth inequality, is adopted to investigate the wealth distribution under infectious disease.Using the feedback control method, two saturated nonlinear incidence rates are obtained to explore the impact of the government contact control measures on epidemic dynamics and wealth distribution.We find that the contact control measures may reduce the peak of the infected fraction and make more people remain uninfected, but prolong the duration of the epidemic and increase wealth inequality.In a closed (an open) economy, the large-time behavior of wealth distribution presents a Pareto tail, and examples of trading propensity depending on wealth suggest that an increase in the savings of the wealthy may increase wealth inequality.In addition, our simulation results illustrate that the government's tax and redistribution measures can alleviate the wealth inequality caused by the contact control and improve the wealth of agents at low and middle levels.

In this paper, we mainly propose a new priori error estimation for the two-dimensional linearly elastic shallow shell equations, which rely on a family of Kirchhoff-Love theories.As the displacement components of the points on the middle surface have different regularities, the nonconforming element for the discretization shallow shell equations is analysed.Then, relying on the enriching operator, a new error estimate of energy norm is given under the regularity assumptionwith any m > 0. Compared with the classic error analysis in other shell literature, convergence order of numerical solution can be controlled by its corresponding approximation error with an arbitrarily high order term, which fills the gap in the computational shell theory.Finally, numerical results for the saddle shell and cylindrical shell confirm the theoretical prediction.

While being concerned with a singularly perturbed linear differential equation subject to integral boundary conditions, the exact solutions, in general, cannot be specified, and the validity of the maximum principle is unassurable.Hence, a problem arises: how to identify the boundary asymptotics more precisely?We develop a rigorous asymptotic method involving recovered boundary data to tackle the problem.A key ingredient of the approach is to transform the "nonlocal" boundary conditions into "local" boundary conditions.Then, we perform an "εlog ε-estimate" to obtain the refined boundary asymptotics of its solutions with respect to the singular perturbation parameter ε.Furthermore, for the inhomogeneous case, diversified asymptotic behaviors including uniform boundedness and asymptotic blow-up are obtained.Numerical simulations and validations are also presented to further support the corresponding theoretical results.

This paper is concerned with the Cauchy problem for one-dimensional unipolar Euler-Poisson equations with time-dependent damping, where the time-asymptotically degenerate damping in the form of - (1+t) u for > 0 with > 0 plays a crucial role for the structure of solutions. The main issue of the paper is to investigate the critical case with = 1. We first prove that, for all cases with > 0 and > 0 (including the critical case of = 1), once the initial data is steep at a point, then the solutions are locally bounded but their derivatives will blow up in finite time, by means of the method of Riemann invariants and the technical convex analysis. Secondly, for the critical case of = 1 with > 7/3, we prove that there exists a unique global solution, once the initial perturbation around the constant steady-state is sufficiently small. In particular, we derive the algebraic convergence rates of the solution to the constant steady-state, which are piecewise, related to the parameter for 7/3 < 3, 3 < 4 and > 4. The adopted method of proof in this critical case is the technical time-weighted energy method and the time-weight depends on the parameter . Finally, we carry out some numerical simulations in two cases for blow-up and global existence, respectively, which numerically confirm our theoretical results.