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Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, publishes original and expository full-length research articles of significant advances in all branches of mathematics, applied mathematics and related fields. All articles should be written to communicate their contents to a broad scientific audience and must meet high standards for scientific content and clarity. After review and acceptance, articles enter production for immediate publication.

ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007, details at AMS.


  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in March, June, September and December.
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  • ERA is a publication of the American Institute of Mathematical Sciences. All rights reserved.

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Some multivariate polynomials for doubled permutations
Bin Han
2021, 29(2) : 1925-1944 doi: 10.3934/era.2020098 +[Abstract](607) +[HTML](287) +[PDF](398.24KB)
The sharp time decay rate of the isentropic Navier-Stokes system in $ {\mathop{\mathbb R\kern 0pt}\nolimits}^3 $
Yuhui Chen, Ronghua Pan and Leilei Tong
2021, 29(2) : 1945-1967 doi: 10.3934/era.2020099 +[Abstract](498) +[HTML](259) +[PDF](461.93KB)
Regular random attractors for non-autonomous stochastic reaction-diffusion equations on thin domains
Dingshi Li and Xuemin Wang
2021, 29(2) : 1969-1990 doi: 10.3934/era.2020100 +[Abstract](451) +[HTML](252) +[PDF](462.41KB)
Computational aspects of the multiscale discontinuous Galerkin method for convection-diffusion-reaction problems
ShinJa Jeong and Mi-Young Kim
2021, 29(2) : 1991-2006 doi: 10.3934/era.2020101 +[Abstract](538) +[HTML](280) +[PDF](1523.36KB)
Decoupling PDE computation with intrinsic or inertial Robin interface condition
Lian Zhang, Mingchao Cai and Mo Mu
2021, 29(2) : 2007-2028 doi: 10.3934/era.2020102 +[Abstract](486) +[HTML](259) +[PDF](3144.54KB)
On $ P_1 $ nonconforming finite element aproximation for the Signorini problem
Mingxia Li, Dongying Hua and Hairong Lian
2021, 29(2) : 2029-2045 doi: 10.3934/era.2020103 +[Abstract](421) +[HTML](242) +[PDF](435.38KB)
Finite/fixed-time synchronization for complex networks via quantized adaptive control
Yu-Jing Shi and Yan Ma
2021, 29(2) : 2047-2061 doi: 10.3934/era.2020104 +[Abstract](608) +[HTML](288) +[PDF](378.87KB)
Asymptotic behavior of the one-dimensional compressible micropolar fluid model
Haibo Cui, Junpei Gao and Lei Yao
2021, 29(2) : 2063-2075 doi: 10.3934/era.2020105 +[Abstract](466) +[HTML](258) +[PDF](358.63KB)
The global supersonic flow with vacuum state in a 2D convex duct
Jintao Li, Jindou Shen and Gang Xu
2021, 29(2) : 2077-2099 doi: 10.3934/era.2020106 +[Abstract](511) +[HTML](265) +[PDF](791.6KB)
A geometric-analytic study of linear differential equations of order two
Víctor León and Bruno Scárdua
2021, 29(2) : 2101-2127 doi: 10.3934/era.2020107 +[Abstract](659) +[HTML](214) +[PDF](456.23KB)
On a model of COVID-19 dynamics
Jorge Rebaza
2021, 29(2) : 2129-2140 doi: 10.3934/era.2020108 +[Abstract](513) +[HTML](234) +[PDF](410.23KB)
Integrating evolution equations using Fredholm determinants
Feride Tığlay
2021, 29(2) : 2141-2147 doi: 10.3934/era.2020109 +[Abstract](376) +[HTML](206) +[PDF](281.76KB)
Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory
Deyue Zhang and Yukun Guo
2021, 29(2) : 2149-2165 doi: 10.3934/era.2020110 +[Abstract](433) +[HTML](214) +[PDF](335.94KB)
More bijections for Entringer and Arnold families
Heesung Shin and Jiang Zeng
2021, 29(2) : 2167-2185 doi: 10.3934/era.2020111 +[Abstract](564) +[HTML](232) +[PDF](435.77KB)
Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays
Meiyu Sui, Yejuan Wang and Peter E. Kloeden
2021, 29(2) : 2187-2221 doi: 10.3934/era.2020112 +[Abstract](454) +[HTML](222) +[PDF](511.36KB)
Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations Special Issues
Matthew Gardner, Adam Larios, Leo G. Rebholz, Duygu Vargun and Camille Zerfas
2020doi: 10.3934/era.2020113 +[Abstract](437) +[HTML](235) +[PDF](5363.96KB)
Solvability of the matrix equation $ AX^{2} = B $ with semi-tensor product Special Issues
Jin Wang, Jun-E Feng and Hua-Lin Huang
2020doi: 10.3934/era.2020114 +[Abstract](422) +[HTML](235) +[PDF](400.64KB)
Propagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearity
Shao-Xia Qiao and Li-Jun Du
2020doi: 10.3934/era.2020116 +[Abstract](359) +[HTML](157) +[PDF](342.93KB)
On projective threefolds of general type with small positive geometric genus
Meng Chen, Yong Hu and Matteo Penegini
2020doi: 10.3934/era.2020117 +[Abstract](336) +[HTML](183) +[PDF](466.62KB)
Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment
Hai-Feng Huo, Shi-Ke Hu and Hong Xiang
2020doi: 10.3934/era.2020118 +[Abstract](365) +[HTML](201) +[PDF](709.18KB)
Refined asymptotic behavior and uniqueness of large solutions to a quasilinear elliptic equation in a borderline case
Yongxiu Shi and Haitao Wan
2020doi: 10.3934/era.2020119 +[Abstract](359) +[HTML](159) +[PDF](353.08KB)
A conforming discontinuous Galerkin finite element method on rectangular partitions Special Issues
Yue Feng, Yujie Liu, Ruishu Wang and Shangyou Zhang
2020doi: 10.3934/era.2020120 +[Abstract](371) +[HTML](164) +[PDF](298.59KB)
On recent progress of single-realization recoveries of random Schrödinger systems Special Issues
Shiqi Ma
2020doi: 10.3934/era.2020121 +[Abstract](352) +[HTML](169) +[PDF](642.99KB)
Continuous subsonic-sonic flows in a two-dimensional semi-infinitely long nozzle Special Issues
Mingjun Zhou and Jingxue Yin
2020doi: 10.3934/era.2020122 +[Abstract](334) +[HTML](170) +[PDF](490.52KB)
Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $ Special Issues
Wenjun Liu, Yukun Xiao and Xiaoqing Yue
2020doi: 10.3934/era.2020123 +[Abstract](420) +[HTML](173) +[PDF](306.09KB)
A generalization on derivations of Lie algebras
Hongliang Chang, Yin Chen and Runxuan Zhang
2020doi: 10.3934/era.2020124 +[Abstract](403) +[HTML](154) +[PDF](397.64KB)
The Brezis-Nirenberg type double critical problem for a class of Schrödinger-Poisson equations
Li Cai and Fubao Zhang
2020doi: 10.3934/era.2020125 +[Abstract](322) +[HTML](141) +[PDF](333.03KB)
Hybridized weak Galerkin finite element methods for Brinkman equations Special Issues
Jiwei Jia, Young-Ju Lee, Yue Feng, Zichan Wang and Zhongshu Zhao
2020doi: 10.3934/era.2020126 +[Abstract](351) +[HTML](148) +[PDF](444.9KB)
A four-field mixed finite element method for Biot's consolidation problems Special Issues
Wenya Qi, Padmanabhan Seshaiyer and Junping Wang
2020doi: 10.3934/era.2020127 +[Abstract](325) +[HTML](140) +[PDF](396.68KB)
Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM Special Issues
Hyung-Chun Lee
2020doi: 10.3934/era.2020128 +[Abstract](306) +[HTML](151) +[PDF](6771.49KB)
Note on coisotropic Floer homology and leafwise fixed points
Fabian Ziltener
2021doi: 10.3934/era.2021001 +[Abstract](226) +[HTML](112) +[PDF](296.46KB)
Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system
Riadh Chteoui, Abdulrahman F. Aljohani and Anouar Ben Mabrouk
2021doi: 10.3934/era.2021002 +[Abstract](366) +[HTML](145) +[PDF](1460.42KB)
Global stability of traveling waves for a spatially discrete diffusion system with time delay
Ting Liu and Guo-Bao Zhang
2021doi: 10.3934/era.2021003 +[Abstract](258) +[HTML](123) +[PDF](362.16KB)
On the universal $ \alpha $-central extensions of the semi-direct product of Hom-preLie algebras
Bing Sun, Liangyun Chen and Yan Cao
2021doi: 10.3934/era.2021004 +[Abstract](207) +[HTML](124) +[PDF](388.95KB)
Tori can't collapse to an interval
Sergio Zamora
2021doi: 10.3934/era.2021005 +[Abstract](215) +[HTML](115) +[PDF](370.74KB)
$ C^* $-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms
Kengo Matsumoto
2021doi: 10.3934/era.2021006 +[Abstract](210) +[HTML](111) +[PDF](299.13KB)
Telescoping method, summation formulas, and inversion pairs Special Issues
Qing-Hu Hou and Yarong Wei
2021doi: 10.3934/era.2021007 +[Abstract](243) +[HTML](135) +[PDF](329.28KB)
Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra Special Issues
Hongyan Guo
2021doi: 10.3934/era.2021008 +[Abstract](239) +[HTML](112) +[PDF](320.19KB)
On $ n $-slice algebras and related algebras Special Issues
Jin-Yun Guo, Cong Xiao and Xiaojian Lu
2021doi: 10.3934/era.2021009 +[Abstract](146) +[HTML](116) +[PDF](538.39KB)
Local well-posedness of perturbed Navier-Stokes system around Landau solutions
Jingjing Zhang and Ting Zhang
2021doi: 10.3934/era.2021010 +[Abstract](135) +[HTML](71) +[PDF](396.95KB)
A multiscale stochastic criminal behavior model under a hybrid scheme Special Issues
Chuntian Wang and Yuan Zhang
2021doi: 10.3934/era.2021011 +[Abstract](137) +[HTML](87) +[PDF](1153.25KB)
An a posteriori error estimator based on least-squares finite element solutions for viscoelastic fluid flows Special Issues
Hsueh-Chen Lee and Hyesuk Lee
2021doi: 10.3934/era.2021012 +[Abstract](274) +[HTML](96) +[PDF](4744.99KB)
Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra Special Issues
Pengliang Xu and Xiaomin Tang
2021doi: 10.3934/era.2021013 +[Abstract](152) +[HTML](97) +[PDF](322.55KB)
Averaging principle on infinite intervals for stochastic ordinary differential equations Special Issues
David Cheban and Zhenxin Liu
2021doi: 10.3934/era.2021014 +[Abstract](169) +[HTML](68) +[PDF](387.01KB)
Ergodic measures of intermediate entropy for affine transformations of nilmanifolds Special Issues
Wen Huang, Leiye Xu and Shengnan Xu
2021doi: 10.3934/era.2021015 +[Abstract](132) +[HTML](71) +[PDF](313.83KB)
A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
Christos Sourdis
2021doi: 10.3934/era.2021016 +[Abstract](126) +[HTML](47) +[PDF](341.7KB)
On a general homogeneous three-dimensional system of difference equations
Nouressadat Touafek, Durhasan Turgut Tollu and Youssouf Akrour
2021doi: 10.3934/era.2021017 +[Abstract](136) +[HTML](57) +[PDF](492.41KB)
Refined Wilf-equivalences by Comtet statistics Special Issues
Shishuo Fu, Zhicong Lin and Yaling Wang
2021doi: 10.3934/era.2021018 +[Abstract](103) +[HTML](47) +[PDF](534.03KB)
Convergence analysis of Fourier pseudo-spectral schemes for three-dimensional incompressible Navier-Stokes equations Special Issues
Cheng Wang
2021doi: 10.3934/era.2021019 +[Abstract](129) +[HTML](49) +[PDF](495.86KB)
Structure of sympathetic Lie superalgebras Special Issues
Yusi Fan, Chenrui Yao and Liangyun Chen
2021doi: 10.3934/era.2021020 +[Abstract](106) +[HTML](50) +[PDF](303.23KB)
On inner Poisson structures of a quantum cluster algebra without coefficients Special Issues
Fang Li and Jie Pan
2021doi: 10.3934/era.2021021 +[Abstract](120) +[HTML](40) +[PDF](308.09KB)
Complexity in time-delay networks of multiple interacting neural groups Special Issues
Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang and Xingyong Li
2021doi: 10.3934/era.2021022 +[Abstract](129) +[HTML](57) +[PDF](3695.69KB)
Big homoclinic orbit bifurcation underlying post-inhibitory rebound spike and a novel threshold curve of a neuron Special Issues
Xianjun Wang, Huaguang Gu and Bo Lu
2021doi: 10.3934/era.2021023 +[Abstract](135) +[HTML](90) +[PDF](2461.63KB)
Global dynamics of the solution for a bistable reaction diffusion equation with nonlocal effect
Meng-Xue Chang, Bang-Sheng Han and Xiao-Ming Fan
2021doi: 10.3934/era.2021024 +[Abstract](123) +[HTML](49) +[PDF](405.63KB)
Picture groups and maximal green sequences Special Issues
Kiyoshi Igusa and Gordana Todorov
2021doi: 10.3934/era.2021025 +[Abstract](128) +[HTML](62) +[PDF](534.52KB)
Instability and bifurcation of a cooperative system with periodic coefficients Special Issues
Tian Hou, Yi Wang and Xizhuang Xie
2021doi: 10.3934/era.2021026 +[Abstract](146) +[HTML](44) +[PDF](807.77KB)
Simultaneous recovery of surface heat flux and thickness of a solid structure by ultrasonic measurements Special Issues
Youjun Deng, Hongyu Liu, Xianchao Wang, Dong Wei and Liyan Zhu
2021doi: 10.3934/era.2021027 +[Abstract](119) +[HTML](52) +[PDF](525.34KB)
Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise
Lianbing She, Nan Liu, Xin Li and Renhai Wang
2021doi: 10.3934/era.2021028 +[Abstract](12) +[HTML](30) +[PDF](624.31KB)
Global behavior of P-dimensional difference equations system
Amira Khelifa and Yacine Halim
2021doi: 10.3934/era.2021029 +[Abstract](30) +[HTML](15) +[PDF](397.48KB)
A C0 interior penalty method for the Cahn-Hilliard equation
Amanda E. Diegel
2021doi: 10.3934/era.2021030 +[Abstract](10) +[HTML](15) +[PDF](942.63KB)
A multigrid based finite difference method for solving parabolic interface problem
Hongsong Feng and Shan Zhao
2021doi: 10.3934/era.2021031 +[Abstract](10) +[HTML](13) +[PDF](18671.43KB)
A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfaces
Derrick Jones and Xu Zhang
2021doi: 10.3934/era.2021032 +[Abstract](14) +[HTML](13) +[PDF](1840.69KB)
Relative mmp without $ \mathbb{Q} $-factoriality
János Kollár
2021doi: 10.3934/era.2021033 +[Abstract](11) +[HTML](9) +[PDF](300.75KB)
Firing patterns and bifurcation analysis of neurons under electromagnetic induction
Qixiang Wen, Shenquan Liu and Bo Lu
2021doi: 10.3934/era.2021034 +[Abstract](9) +[HTML](7) +[PDF](6539.09KB)
Enhancement of gamma oscillations in E/I neural networks by increase of difference between external inputs
Xiaochun Gu, Fang Han, Zhijie Wang, Kaleem Kashif and Wenlian Lu
2021doi: 10.3934/era.2021035 +[Abstract](11) +[HTML](7) +[PDF](1044.39KB)
Non-existence of solutions to some degenerate coercivity elliptic equations involving measures data
Maoji Ri, Shuibo Huang and Canyun Huang
2020, 28: 165-182 doi: 10.3934/era.2020011 +[Abstract](886) +[HTML](414) +[PDF](392.76KB) Cited By(4)
Strong $ (L^2,L^\gamma\cap H_0^1) $-continuity in initial data of nonlinear reaction-diffusion equation in any space dimension
Hongyong Cui, Peter E. Kloeden and Wenqiang Zhao
2020, 28: 1357-1374 doi: 10.3934/era.2020072 +[Abstract](638) +[HTML](323) +[PDF](384.95KB) Cited By(3)
On the mutual singularity of multifractal measures
Zied Douzi and Bilel Selmi
2020, 28: 423-432 doi: 10.3934/era.2020024 +[Abstract](760) +[HTML](277) +[PDF](324.42KB) Cited By(3)
On the time decay in phase–lag thermoelasticity with two temperatures
Antonio Magaña, Alain Miranville and Ramón Quintanilla
2019, 27: 7-19 doi: 10.3934/era.2019007 +[Abstract](1600) +[HTML](757) +[PDF](365.4KB) Cited By(3)
Rough semi-uniform spaces and its image proximities
Surabhi Tiwari and Pankaj Kumar Singh
2020, 28: 1095-1106 doi: 10.3934/era.2020060 +[Abstract](635) +[HTML](374) +[PDF](3941.13KB) Cited By(2)
A multiple-relaxation-time lattice Boltzmann method with Beam-Warming scheme for a coupled chemotaxis-fluid model
Zhonghua Qiao and Xuguang Yang
2020, 28: 1207-1225 doi: 10.3934/era.2020066 +[Abstract](663) +[HTML](314) +[PDF](1610.81KB) Cited By(2)
Well-posed final value problems and Duhamel's formula for coercive Lax–Milgram operators
Jon Johnsen
2019, 27: 20-36 doi: 10.3934/era.2019008 +[Abstract](1339) +[HTML](667) +[PDF](448.4KB) Cited By(2)
Some multivariate polynomials for doubled permutations
Bin Han
2021, 29: 1925-1944 doi: 10.3934/era.2020098 +[Abstract](607) +[HTML](287) +[PDF](398.24KB) Cited By(2)
Some recent progress on inverse scattering problems within general polyhedral geometry
Xinlin Cao, Huaian Diao and Jinhong Li
2021, 29: 1753-1782 doi: 10.3934/era.2020090 +[Abstract](621) +[HTML](338) +[PDF](492.02KB) Cited By(2)
New series for powers of $ \pi $ and related congruences
Zhi-Wei Sun
2020, 28: 1273-1342 doi: 10.3934/era.2020070 +[Abstract](618) +[HTML](371) +[PDF](571.91KB) Cited By(2)
A conjecture on cluster automorphisms of cluster algebras
Peigen Cao, Fang Li, Siyang Liu and Jie Pan
2019, 27: 1-6 doi: 10.3934/era.2019006 +[Abstract](1845) +[HTML](810) +[PDF](313.13KB) PDF Downloads(362)
$ H^2 $ blowup result for a Schrödinger equation with nonlinear source term
Xuan Liu and Ting Zhang
2020, 28: 777-794 doi: 10.3934/era.2020039 +[Abstract](758) +[HTML](549) +[PDF](392.34KB) PDF Downloads(280)
Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence
Yang Yang, Yun-Rui Yang and Xin-Jun Jiao
2020, 28: 1-13 doi: 10.3934/era.2020001 +[Abstract](1286) +[HTML](591) +[PDF](369.78KB) PDF Downloads(280)
The global conservative solutions for the generalized camassa-holm equation
Li Yang, Chunlai Mu, Shouming Zhou and Xinyu Tu
2019, 27: 37-67 doi: 10.3934/era.2019009 +[Abstract](1311) +[HTML](618) +[PDF](562.79KB) PDF Downloads(275)
A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction
Zexuan Liu, Zhiyuan Sun and Jerry Zhijian Yang
2020, 28: 1487-1501 doi: 10.3934/era.2020078 +[Abstract](733) +[HTML](330) +[PDF](5508.22KB) PDF Downloads(272)
On a final value problem for a nonlinear fractional pseudo-parabolic equation
Vo Van Au, Hossein Jafari, Zakia Hammouch and Nguyen Huy Tuan
2021, 29: 1709-1734 doi: 10.3934/era.2020088 +[Abstract](1002) +[HTML](258) +[PDF](484.76KB) PDF Downloads(267)
Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems
Xiaoqiang Dai, Chao Yang, Shaobin Huang, Tao Yu and Yuanran Zhu
2020, 28: 91-102 doi: 10.3934/era.2020006 +[Abstract](1269) +[HTML](635) +[PDF](299.33KB) PDF Downloads(251)
Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces
Muwafaq Salih and Árpád Száz
2020, 28: 471-548 doi: 10.3934/era.2020027 +[Abstract](935) +[HTML](560) +[PDF](771.11KB) PDF Downloads(240)
The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term
Gongwei Liu
2020, 28: 263-289 doi: 10.3934/era.2020016 +[Abstract](900) +[HTML](374) +[PDF](383.54KB) PDF Downloads(237)
Global existence and propagation speed for a Degasperis-Procesi equation with both dissipation and dispersion
Guenbo Hwang and Byungsoo Moon
2020, 28: 15-25 doi: 10.3934/era.2020002 +[Abstract](1183) +[HTML](604) +[PDF](327.55KB) PDF Downloads(236)

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