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Optimal regularity of positive solutions of the Hénon-Hardy equation and related equations

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Science China Mathematics 2024年第10期67卷 2283-2302页

作者： Zongming Guo Fangshu Wan college of Mathematics and Information Science Henan Normal UniversityXinxiang 453007China School of mathematical sciences University of Science and Technology of ChinaHefei 230026China School of mathematical sciences Anhui UniversityHefei 230601China

We present a new method to determine the optimal regularity of positive solutions u∈C^(4)(Ω\{0})∩C^(0)(Ω) of the Hénon-Hardy equation,i.e.,Δ^(2)u=|x|^(α)u^(p)inΩ,(0,1) where Ω■RN(N≥4) is a bounded smooth domain with 0∈Ω,α>-4,and p∈*** is clear that 0 is an isolated singular point of solutions of(0.1) and the optimal regularity of u in Ω relies on the parameter α.It is also important to see that the regularity of u at x=0 determines the regularity of u in Ω.We first establish asymptotic expansions up to arbitrary orders at x=0 of prescribed positive solutions u ∈C^(4)(Ω{0}) ∩ C^(0)(Ω)of(0.1).Then we show that the regularity at x=0 of each positive solution u of(0.1) can be determined by some terms in asymptotic expansions of the related positive radial solution of the equation(0.1) with Ω=B,where B is the unit ball of R^(N).The main idea works for more general equations with singular weights.

关键词： H´enon-Hardy equation positive solutions optimal regularity singular point asymptotic expansions

Cross-diffusion induced Turing instability of Hopf bifurcating periodic solutions in the reaction-diffusion enzyme reaction model

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International Journal of Biomathematics 2024年第4期17卷 133-150页

作者： Haicheng Liu Wenshuo Yuan Bin Ge Jihong Shen college of mathematical sciences Harbin Engineering University Harbin 150001 HeilongjiangP.R.China

Aiming at the spatial pattern phenomenon in biochemical reactions,an enzyme-reaction Sporns-Seelig model with cross-diffusion is chosen as study *** the central manifold theory,normal form method,local Hopf bifurcation theorem and perturbation theory,we study Turing instability of the spatially homogeneous Hopf bifurcation periodic *** last,the theoretical results are verified by numerical simulations.

关键词： Sporns-Seelig model diffusion Hopf bifurcation periodic solutions Turing instability

Chimera states of phase oscillator populations with nonlocal higher-order couplings

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Chinese Physics B 2024年第4期33卷 402-407页

作者：伍勇刚余华健郑志刚徐灿 School of mathematical sciences Huaqiao UniversityQuanzhou 362021China Institute of Systems Science and college of Information Science and Engineering Huaqiao UniversityXiamen 361021China

The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical ***, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial *** works have shown that higher-order interactions promote coherent ***, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent ***, we identify that the chimera states arise as a result of multi-attractors in dynamic ***, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera *** the observed results can be well described in terms of the dimension reduction *** study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.

关键词： synchronization complex system coupled oscillators phase transition

2-local unstable homotopy groups of indecomposable A3～2-complexes

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Science China Mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan college of Mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of Mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of mathematical sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A3～*** main technique used is analysing the homotopy property of J（A,X）,defined by Gray（1973） for a CW-pair（X,A）,which is homoto... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 358-378页

作者： Jin-yan ZHU Yong CHEN School of mathematical sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200062China college of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

The Gerdjikov-Ivanov(GI)hierarchy is derived via recursion operator,in this article,we mainly investigate the third-order flow GI *** the framework of the Riemann-Hilbert method,the soliton matrices of the third-order flow GI equation with simple zeros and elementary high-order zeros of Riemann-Hilbert problem are constructed through the standard dressing *** advantage of this result,some properties and asymptotic analysis of single soliton solution and two soliton solution are discussed,and the simple elastic interaction of two soliton are *** with soliton solution of the classical second-order flow,we find that the higher-order dispersion term affects the propagation velocity,propagation direction and amplitude of the ***,by means of a certain limit technique,the high-order soliton solution matrix for the third-order flow GI equation is derived.

关键词： Gerdjikov-Ivanov hierarchy third-order flow GI equation Riemann-Hilbert method high-order soliton

Oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions via Prufer transformation

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 191-200页

作者： LI Zhi-yu LI Kun CAI Jin-ming QIN Jian-fang ZHENG Zhao-wen School of mathematical sciences Qufu Normal UniversityQufu 273165China college of Mathematics and Systems Science Guangdong Polytechnic Normal UniversityGuangzhou 510665China

A class of Sturm-Liouville problems with discontinuity is studied in this *** oscillation properties of eigenfunctions for Sturm-Liouville problems with interface conditions are *** main method used in this paper is based on Prufer transformation,which is different from the classical ***,we give two examples to verify our main results.

关键词： Sturm-Liouville problem interface condition oscillatory solution

On the superconvergence of a WG method for the elliptic problem with variable coefficients

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Science China Mathematics 2024年第8期67卷 1899-1910页

作者： Junping Wang Xiaoshen Wang Xiu Ye Shangyou Zhang Peng Zhu Division of mathematical sciences National Science FoundationAlexandriaVA 22314USA Department of Mathematics University of Arkansas at Little RockLittle RockAR 72204USA Department of mathematical sciences University of DelawareNewarkDE 19716USA college of Data Science Jiaxing UniversityJiaxing 314001China

This article extends a recently developed superconvergence result for weak Galerkin(WG)approximations for modeling partial differential equations from constant coefficients to variable *** superconvergence features a rate that is two orders higher than the optimal-order error estimates in the usual energy and L^(2)*** extension from constant to variable coefficients for the modeling equations is highly *** underlying technical analysis is based on a sequence of projections and *** results confirm the superconvergence theory for second-order elliptic problems with variable coefficients.

关键词： weak Galerkin finite element methods superconvergence second-order elliptic problems stabilizerfree

Optimal control of differential quasivariational-hemivariational inequalities with applications

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Science China Mathematics 2024年第11期67卷 2587-2606页

作者： Dong-ling Cai Stanis?aw Migórski Yi-bin Xiao School of mathematical sciences University of Electronic Science and Technology of China college of Applied Mathematics Chengdu University of Information Technology Chair of Optimization and Control Jagiellonian University in Krakow

In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic *** problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent ***,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the ***,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of *** all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent ***,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.

关键词： differential variational-hemivariational inequality unilateral constraint history-dependent operator optimal control time-optimal control maximum stay problem

The effect of salt anion in ether‐based electrolyte for electrochemical performance of sodium‐ion batteries:A case study of hard carbon

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Carbon Energy 2024年第8期6卷 285-297页

作者： Jiabao Li Jingjing Hao Quan Yuan Ruoxing Wang Frederick Marlton Tianyi Wang Chengyin Wang Xin Guo Guoxiu Wang college of Chemistry and Chemical Engineering Yangzhou UniversityYangzhouJiangsuChina School of mathematical and Physical sciences Centre for Clean Energy TechnologyFaculty of ScienceUniversity of Technology SydneySydneyAustralia

Compared with the extensively used ester‐based electrolyte,the hard carbon(HC)electrode is more compatible with the ether‐based counterpart in sodium‐ion batteries,which can lead to improved cycling stability and robust rate ***,the impact of salt anion on the electrochemical performance of HC electrodes has yet to be fully *** this study,the anionic chemistry in regulating the stability of electrolytes and the performance of sodium‐ion batteries have been systematically *** work shows discrepancies in the reductive stability of the anionic group,redox kinetics,and component/structure of solid electrolyte interface(SEI)with different salts(NaBF_(4),NaPF_(6),and NaSO_(3)CF_(3))in the typical ether solvent(diglyme).Particularly,the density functional theory calculation manifests the preferred decomposition of PF_(6)−due to the reduced reductive stability of anions in the solvation structure,thus leading to the formation of NaF‐rich *** investigation on redox kinetics reveals that the NaPF_(6)/diglyme can induce the fast ionic diffusion dynamic and low charge transfer barrier for HC electrode,thus resulting in superior sodium storage performance in terms of rate capability and cycling life,which outperforms those of NaBF_(4)/diglyme and NaSO_(3)CF_(3)/***,this work offers valuable insights for optimizing the electrochemical behaviors of electrode materials by regulating the anionic group in the electrolyte.

关键词： ether‐based electrolyte reaction kinetics salt anion SEI components sodium storage