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Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical 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.


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The longtime behavior of the model with nonlocal diffusion and free boundaries in online social networks
Meng Zhao
2020, 28(3) : 1143-1160 doi: 10.3934/era.2020063 +[Abstract](405) +[HTML](157) +[PDF](346.33KB)
The Jacobi spectral collocation method for fractional integro-differential equations with non-smooth solutions
Yin Yang, Sujuan Kang and Vasiliy I. Vasil'ev
2020, 28(3) : 1161-1189 doi: 10.3934/era.2020064 +[Abstract](447) +[HTML](180) +[PDF](640.45KB)
Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model
Jiangshan Wang, Lingxiong Meng and Hongen Jia
2020, 28(3) : 1191-1205 doi: 10.3934/era.2020065 +[Abstract](325) +[HTML](157) +[PDF](361.28KB)
A multiple-relaxation-time lattice Boltzmann method with Beam-Warming scheme for a coupled chemotaxis-fluid model
Zhonghua Qiao and Xuguang Yang
2020, 28(3) : 1207-1225 doi: 10.3934/era.2020066 +[Abstract](360) +[HTML](148) +[PDF](1610.81KB)
Colimits of crossed modules in modified categories of interest
Ali Aytekin and Kadir Emir
2020, 28(3) : 1227-1238 doi: 10.3934/era.2020067 +[Abstract](315) +[HTML](134) +[PDF](324.17KB)
On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements
Xiaoping Fang, Youjun Deng, Wing-Yan Tsui and Zaiyun Zhang
2020, 28(3) : 1239-1255 doi: 10.3934/era.2020068 +[Abstract](330) +[HTML](149) +[PDF](367.52KB)
Recent progress on the mathematical study of anomalous localized resonance in elasticity
Hongjie Li
2020, 28(3) : 1257-1272 doi: 10.3934/era.2020069 +[Abstract](295) +[HTML](163) +[PDF](361.94KB)
New series for powers of $ \pi $ and related congruences
Zhi-Wei Sun
2020, 28(3) : 1273-1342 doi: 10.3934/era.2020070 +[Abstract](362) +[HTML](214) +[PDF](571.91KB)
The boundedness and upper semicontinuity of the pullback attractors for a 2D micropolar fluid flows with delay
Wenlong Sun
2020, 28(3) : 1343-1356 doi: 10.3934/era.2020071 +[Abstract](307) +[HTML](154) +[PDF](352.36KB)
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(3) : 1357-1374 doi: 10.3934/era.2020072 +[Abstract](323) +[HTML](142) +[PDF](384.95KB)
The regularized Boussinesq equations with partial dissipations in dimension two
Hua Qiu and Zheng-An Yao
2020doi: 10.3934/era.2020073 +[Abstract](240) +[HTML](121) +[PDF](355.71KB)
The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay
Xin-Guang Yang, Lu Li, Xingjie Yan and Ling Ding
2020doi: 10.3934/era.2020074 +[Abstract](230) +[HTML](114) +[PDF](393.79KB)
A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior
Yichen Zhang and Meiqiang Feng
2020doi: 10.3934/era.2020075 +[Abstract](256) +[HTML](118) +[PDF](380.87KB)
A robust adaptive grid method for singularly perturbed Burger-Huxley equations
Li-Bin Liu, Ying Liang, Jian Zhang and Xiaobing Bao
2020doi: 10.3934/era.2020076 +[Abstract](257) +[HTML](222) +[PDF](443.1KB)
Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems
Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li and Shang Liu
2020doi: 10.3934/era.2020077 +[Abstract](272) +[HTML](120) +[PDF](2184.37KB)
A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction
Zexuan Liu, Zhiyuan Sun and Jerry Zhijian Yang
2020doi: 10.3934/era.2020078 +[Abstract](280) +[HTML](126) +[PDF](5491.27KB)
Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium
Xuefei He, Kun Wang and Liwei Xu
2020doi: 10.3934/era.2020079 +[Abstract](245) +[HTML](127) +[PDF](1362.43KB)
Odd random attractors for stochastic non-autonomous Kuramoto-Sivashinsky equations without dissipation
Yangrong Li, Shuang Yang and Qiangheng Zhang
2020doi: 10.3934/era.2020080 +[Abstract](219) +[HTML](112) +[PDF](340.05KB)
Global weak solutions for the two-component Novikov equation
Cheng He and Changzheng Qu
2020doi: 10.3934/era.2020081 +[Abstract](257) +[HTML](133) +[PDF](394.37KB)
Gorenstein global dimensions relative to balanced pairs
Haiyu Liu, Rongmin Zhu and Yuxian Geng
2020doi: 10.3934/era.2020082 +[Abstract](223) +[HTML](117) +[PDF](294.33KB)
Regularity criteria for weak solutions of the Magneto-micropolar equations
Jens Lorenz, Wilberclay G. Melo and Suelen C. P. de Souza
2020doi: 10.3934/era.2020083 +[Abstract](205) +[HTML](89) +[PDF](403.7KB)
Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting
Kerioui Nadjah and Abdelouahab Mohammed Salah
2020doi: 10.3934/era.2020084 +[Abstract](196) +[HTML](84) +[PDF](802.19KB)
Threshold dynamics of stochastic models with time delays: A case study for yunnan, China
Zhimin Li, Tailei Zhang and Xiuqing Li
2020doi: 10.3934/era.2020085 +[Abstract](150) +[HTML](91) +[PDF](370.72KB)
Some properties for almost cellular algebras
Yongjie Wang and Nan Gao
2020doi: 10.3934/era.2020086 +[Abstract](162) +[HTML](96) +[PDF](320.65KB)
Global conservative solutions for a modified periodic coupled Camassa-Holm system
Rong Chen, Shihang Pan and Baoshuai Zhang
2020doi: 10.3934/era.2020087 +[Abstract](155) +[HTML](76) +[PDF](398.08KB)
On a final value problem for a nonlinear fractional pseudo-parabolic equation
Vo Van Au, Hossein Jafari, Zakia Hammouch and Nguyen Huy Tuan
2020doi: 10.3934/era.2020088 +[Abstract](285) +[HTML](71) +[PDF](569.04KB)
Error estimates for second-order SAV finite element method to phase field crystal model Special Issues
Liupeng Wang and Yunqing Huang
2020doi: 10.3934/era.2020089 +[Abstract](221) +[HTML](94) +[PDF](944.15KB)
Some recent progress on inverse scattering problems within general polyhedral geometry Special Issues
Xinlin Cao, Huaian Diao and Jinhong Li
2020doi: 10.3934/era.2020090 +[Abstract](167) +[HTML](121) +[PDF](481.37KB)
Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello and Marko A. Rojas-Medar
2020doi: 10.3934/era.2020091 +[Abstract](121) +[HTML](47) +[PDF](406.98KB)
Combinatorics of some fifth and sixth order mock theta functions
Meenakshi Rana and Shruti Sharma
2020doi: 10.3934/era.2020092 +[Abstract](103) +[HTML](59) +[PDF](322.37KB)
A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations Special Issues
Guoliang Zhang, Shaoqin Zheng and Tao Xiong
2020doi: 10.3934/era.2020093 +[Abstract](173) +[HTML](116) +[PDF](505.13KB)
Skew doubled shifted plane partitions: Calculus and asymptotics
Guo-Niu Han and Huan Xiong
2020doi: 10.3934/era.2020094 +[Abstract](105) +[HTML](46) +[PDF](352.3KB)
Two-grid method for semiconductor device problem by mixed finite element method and characteristics finite element method Special Issues
Ying Liu, Yanping Chen, Yunqing Huang and Yang Wang
2020doi: 10.3934/era.2020095 +[Abstract](152) +[HTML](59) +[PDF](2279.76KB)
Viscosity robust weak Galerkin finite element methods for Stokes problems Special Issues
Bin Wang and Lin Mu
2020doi: 10.3934/era.2020096 +[Abstract](127) +[HTML](54) +[PDF](1236.25KB)
A weak Galerkin finite element method for nonlinear conservation laws Special Issues
Xiu Ye, Shangyou Zhang and Peng Zhu
2020doi: 10.3934/era.2020097 +[Abstract](131) +[HTML](63) +[PDF](413.06KB)
Some multivariate polynomials for doubled permutations Special Issues
Bin Han
2020doi: 10.3934/era.2020098 +[Abstract](122) +[HTML](56) +[PDF](374.51KB)
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
2020doi: 10.3934/era.2020099 +[Abstract](81) +[HTML](47) +[PDF](444.77KB)
Regular random attractors for non-autonomous stochastic reaction-diffusion equations on thin domains Special Issues
Dingshi Li and Xuemin Wang
2020doi: 10.3934/era.2020100 +[Abstract](74) +[HTML](37) +[PDF](446.01KB)
Computational aspects of the multiscale discontinuous Galerkin method for convection-diffusion-reaction problems Special Issues
ShinJa Jeong and Mi-Young Kim
2020doi: 10.3934/era.2020101 +[Abstract](86) +[HTML](49) +[PDF](1500.19KB)
Decoupling PDE computation with intrinsic or inertial Robin interface condition Special Issues
Lian Zhang, Mingchao Cai and Mo Mu
2020doi: 10.3934/era.2020102 +[Abstract](96) +[HTML](44) +[PDF](3128.15KB)
On $ P_1 $ nonconforming finite element aproximation for the Signorini problem Special Issues
Mingxia Li, Dongying Hua and Hairong Lian
2020doi: 10.3934/era.2020103 +[Abstract](71) +[HTML](42) +[PDF](425.02KB)
Finite/fixed-time synchronization for complex networks via quantized adaptive control Special Issues
Yu-Jing Shi and Yan Ma
2020doi: 10.3934/era.2020104 +[Abstract](209) +[HTML](53) +[PDF](355.02KB)
Asymptotic behavior of the one-dimensional compressible micropolar fluid model Special Issues
Haibo Cui, Junpei Gao and Lei Yao
2020doi: 10.3934/era.2020105 +[Abstract](81) +[HTML](44) +[PDF](342.13KB)
The global supersonic flow with vacuum state in a 2D convex duct Special Issues
Jintao Li, Jindou Shen and Gang Xu
2020doi: 10.3934/era.2020106 +[Abstract](118) +[HTML](57) +[PDF](775.38KB)
A geometric-analytic study of linear differential equations of order two
Víctor León and Bruno Scárdua
2020doi: 10.3934/era.2020107 +[Abstract](44) +[HTML](12) +[PDF](439.97KB)
On a model of COVID-19 dynamics
Jorge Rebaza
2020doi: 10.3934/era.2020108 +[Abstract](26) +[HTML](12) +[PDF](393.41KB)
Integrating evolution equations using Fredholm determinants Special Issues
Feride Tığlay
2020doi: 10.3934/era.2020109 +[Abstract](23) +[HTML](10) +[PDF](264.92KB)
Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory Special Issues
Deyue Zhang and Yukun Guo
2020doi: 10.3934/era.2020110 +[Abstract](21) +[HTML](9) +[PDF](311.95KB)
More bijections for Entringer and Arnold families Special Issues
Heesung Shin and Jiang Zeng
2020doi: 10.3934/era.2020111 +[Abstract](94) +[HTML](15) +[PDF](418.67KB)
Pullback attractors for stochastic recurrent neural networks with discrete and distributed delays Special Issues
Meiyu Sui, Yejuan Wang and Peter E. Kloeden
2020doi: 10.3934/era.2020112 +[Abstract](26) +[HTML](21) +[PDF](494.53KB)
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](29) +[HTML](10) +[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](29) +[HTML](9) +[PDF](400.64KB)
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](483) +[HTML](241) +[PDF](392.76KB) Cited By(3)
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](941) +[HTML](468) +[PDF](448.4KB) Cited By(2)
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](1215) +[HTML](547) +[PDF](365.4KB) Cited By(2)
A note on sign-changing solutions for the Schrödinger Poisson system
Hui Guo and Tao Wang
2020, 28: 195-203 doi: 10.3934/era.2020013 +[Abstract](567) +[HTML](280) +[PDF](332.0KB) Cited By(1)
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](805) +[HTML](426) +[PDF](327.55KB) Cited By(1)
Rough semi-uniform spaces and its image proximities
Surabhi Tiwari and Pankaj Kumar Singh
2020, 28: 1095-1106 doi: 10.3934/era.2020060 +[Abstract](297) +[HTML](170) +[PDF](3941.13KB) Cited By(1)
Weak approximative compactness of hyperplane and Asplund property in Musielak-Orlicz-Bochner function spaces
Shaoqiang Shang and Yunan Cui
2020, 28: 327-346 doi: 10.3934/era.2020019 +[Abstract](427) +[HTML](223) +[PDF](358.13KB) Cited By(1)
New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory
Wenjun Liu, Zhijing Chen and Zhiyu Tu
2020, 28: 433-457 doi: 10.3934/era.2020025 +[Abstract](512) +[HTML](231) +[PDF](421.49KB) Cited By(1)
High-order energy stable schemes of incommensurate phase-field crystal model
Kai Jiang and Wei Si
2020, 28: 1077-1093 doi: 10.3934/era.2020059 +[Abstract](268) +[HTML](115) +[PDF](3164.56KB) Cited By(1)
New series for powers of $ \pi $ and related congruences
Zhi-Wei Sun
2020, 28: 1273-1342 doi: 10.3934/era.2020070 +[Abstract](362) +[HTML](214) +[PDF](571.91KB) Cited By(1)
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](1448) +[HTML](631) +[PDF](313.13KB) PDF Downloads(318)
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](891) +[HTML](419) +[PDF](369.78KB) PDF Downloads(235)
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](952) +[HTML](442) +[PDF](562.79KB) PDF Downloads(234)
$ 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](423) +[HTML](312) +[PDF](392.34KB) PDF Downloads(231)
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](805) +[HTML](426) +[PDF](327.55KB) PDF Downloads(200)
A numerical study of superconvergence of the discontinuous Galerkin method by patch reconstruction
Zexuan Liu, Zhiyuan Sun and Jerry Zhijian Yang
2020, 0: 0 doi: 10.3934/era.2020078 +[Abstract](280) +[HTML](126) +[PDF](5491.27KB) PDF Downloads(198)
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](797) +[HTML](413) +[PDF](299.33KB) PDF Downloads(194)
Two congruences concerning Apéry numbers conjectured by Z.-W. Sun
Chen Wang
2020, 28: 1063-1075 doi: 10.3934/era.2020058 +[Abstract](341) +[HTML](150) +[PDF](312.55KB) PDF Downloads(189)
Initial boundary value problem for a inhomogeneous pseudo-parabolic equation
Jun Zhou
2020, 28: 67-90 doi: 10.3934/era.2020005 +[Abstract](815) +[HTML](419) +[PDF](777.08KB) PDF Downloads(188)
The existence of solutions for a shear thinning compressible non-Newtonian models
Yukun Song, Yang Chen, Jun Yan and Shuai Chen
2020, 28: 47-66 doi: 10.3934/era.2020004 +[Abstract](760) +[HTML](415) +[PDF](413.61KB) PDF Downloads(175)

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