Global Existence of Solutions and Lower Bound Estimate of Blow-Up Time for the Keller-Segel Chemotaxis Model北大核心CSCD

A macroscopic nonlinear Keller-Segel model for chemotactic cell migration was considered, where the existence region of the model is a bounded convex one on Ω ⊂ RN(N≥2). The global existence of the solution on Ω ⊂ R3 was obtained by means of the energy estimate method. The lower bound of the blow-up time was proved for N = 3 and N = 2. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses北大核心CSCD

研究了任意梯度变化的变厚度各向异性转动圆盘的弹性问题.假设圆盘绕刚性轴匀速转动,其材料性能和厚度沿径向任意梯度变化.考虑圆盘在中心转轴处受位移约束,外侧自由,根据各向异性转动圆盘的平衡微分方程,得到关于径向应力的Fredholm积分方程,继而通过对Fredholm积分方程进行数值求解,得到结构的位移场和应力场.对具体梯度变化情况仅需代入相应梯度变化进行求解即可.数值算例部分,通过假设厚度、弹性模量等参数为特殊的幂函数形式,将由Fredholm积分方程求出的数值解与对应的精确解进行对比,以及针对常见的Voigt模型,将由该方法算得的数值解和ANSYS有限元计算结果进行对比,验证了该方法的准确性和精度.其次,针对Voigt模型,重点分析了厚度变化、材料性能梯度参数、各向异性度等对应力场和位移场的影响.提出了针对材料性能和厚度沿径向呈任意梯度变化的圆盘结构弹性分析方法,将为优化功能梯度圆盘的结构和材料参数、有效调整构件应力分布、提高结构安全性,提供强有力的工具;算例分析结果对功能梯度圆盘在复杂条件下的结构安全设计有重要的理论指导意义.     

聚氨酯／聚甲基丙烯酸甲酯互穿聚合物网络的研究

本文对(蓖麻油-聚乙二醇)聚氨酯/聚甲基丙烯酸甲酯(PU/PMMA)互穿聚合物网络(IPN)体系进行了研究.实验结果表明:IPN的力学性能受网络化学构型控制.在PU/PMMA为25/75时,应力-应变曲线出现屈服点,产生类似皮革行为,并在此点抗张强度最高,表现明显的协同效应.动态力学性能及电镜均证明该体系相分离十分严重,通过加入扩链剂及网间交联剂能显著改善两组分相容性,其中网间交联剂效果最好。     

The finite steps of convergence of the fast thresholding algorithms with f-feedbacks in compressed sensing

Numerical Algorithms - Iterative algorithms based on thresholding, feedback, and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and efficient, particularly for...     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Kurdyka–Łojasiewicz Exponent via Inf-projection

Foundations of Computational Mathematics - Kurdyka–Łojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In...     

An approach for solving fuzzy multi-criteria decision problem under linguistic information

Fuzzy Optimization and Decision Making - Linguistic information processing exists in multi-criteria decision making, and linguistic truth-valued lattice implication algebra (LTV-LIA) has definite...     

Monge-Ampère Equation with Bounded Periodic Data

We consider the Monge-Ampère equation det $(D^2u) = f$ in $\mathbb{R}^n,$ where $f$ is a positive bounded periodic function. We prove that $u$ must be the sum of a quadratic polynomial and a periodic function. For $f ≡ 1,$ this is the classic result by Jörgens, Calabi and Pogorelov. For $f ∈ C^α,$ this was proved by Caffarelli and the first named author.     

Fast projection onto the ordered weighted ℓ1 norm ball

In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weighted?₁(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.     

Global axisymmetric classical solutions of full compressible magnetohydrodynamic equations with vacuum free boundary and large initial data

In this paper,the global existence of the classical solution to the vacuum free boundary problem of full compressible magnetohydrodynamic equations with large initial data and axial symmetry is studied.The solutions to the system(1.6)–(1.8) are in the class of radius-dependent solutions,i.e.,independent of the axial variable and the angular variable.In particular,the expanding rate of the moving boundary is obtained.The main difficulty of this problem lies in the strong coupling of the magnetic field,velocity,temperature and the degenerate density near the free boundary.We overcome the obstacle by establishing the lower bound of the temperature by using different Lagrangian coordinates,and deriving the uniform-in-time upper and lower bounds of the Lagrangian deformation variable r;by weighted estimates,and also the uniform-in-time weighted estimates of the higher-order derivatives of solutions by delicate analysis.