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As ERA is getting migrated to Open Access, EditFlow will stop accepting submissions on October 15, 2021. Future submissions will be at the journal’s New Site.

Ever since ERA was created by the American Mathematical Society in 1995, the journal has been serving well the community, with its full contents free of charge for both readers/libraries and authors. This has been an extraordinary contribution to the community by AMS and AIMS for over 20 years. To ensure the sustainability of the journal, ERA will be Open Access beginning in 2022. However, any article submitted in 2021 will not result in APC.

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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 policies outlined in our Ethical Standards.
  • Publishes 6 issues a year in March, June, August, September, November and December.
  • ERA is a free access publication.
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  • ERA is a publication of the American Institute of Mathematical Sciences. All rights reserved.

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Well-posedness results and blow-up for a semi-linear time fractional diffusion equation with variable coefficients
Vo Van Au, Jagdev Singh and Anh Tuan Nguyen
2021, 29(6) : 3581-3607 doi: 10.3934/era.2021052 +[Abstract](720) +[HTML](201) +[PDF](489.64KB)
A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal mesh
Xiu Ye and Shangyou Zhang
2021, 29(6) : 3609-3627 doi: 10.3934/era.2021053 +[Abstract](393) +[HTML](211) +[PDF](5398.53KB)
A simple virtual element-based flux recovery on quadtree
Shuhao Cao
2021, 29(6) : 3629-3647 doi: 10.3934/era.2021054 +[Abstract](411) +[HTML](230) +[PDF](825.67KB)
On blowup of secant varieties of curves
Lawrence Ein, Wenbo Niu and Jinhyung Park
2021, 29(6) : 3649-3654 doi: 10.3934/era.2021055 +[Abstract](434) +[HTML](245) +[PDF](311.11KB)
Regularity of Wong-Zakai approximation for non-autonomous stochastic quasi-linear parabolic equation on $ {\mathbb{R}}^N $
Guifen Liu and Wenqiang Zhao
2021, 29(6) : 3655-3686 doi: 10.3934/era.2021056 +[Abstract](388) +[HTML](183) +[PDF](463.03KB)
Semilinear pseudo-parabolic equations on manifolds with conical singularities
Yitian Wang, Xiaoping Liu and Yuxuan Chen
2021, 29(6) : 3687-3720 doi: 10.3934/era.2021057 +[Abstract](438) +[HTML](188) +[PDF](511.79KB)
Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations
Denghui Wu and Zhen-Hui Bu
2021, 29(6) : 3721-3740 doi: 10.3934/era.2021058 +[Abstract](443) +[HTML](178) +[PDF](436.37KB)
Constructions of three kinds of Bihom-superalgebras
Ying Hou and Liangyun Chen
2021, 29(6) : 3741-3760 doi: 10.3934/era.2021059 +[Abstract](326) +[HTML](180) +[PDF](401.3KB)
Uniqueness and nondegeneracy of positive solutions to an elliptic system in ecology
Zaizheng Li and Zhitao Zhang
2021, 29(6) : 3761-3774 doi: 10.3934/era.2021060 +[Abstract](361) +[HTML](185) +[PDF](382.84KB)
Weighted fourth order elliptic problems in the unit ball
Zongming Guo and Fangshu Wan
2021, 29(6) : 3775-3803 doi: 10.3934/era.2021061 +[Abstract](354) +[HTML](187) +[PDF](438.28KB)
Recent progress on stable and finite Morse index solutions of semilinear elliptic equations
Kelei Wang
2021, 29(6) : 3805-3816 doi: 10.3934/era.2021062 +[Abstract](454) +[HTML](254) +[PDF](332.06KB)
On mathematical analysis of complex fluids in active hydrodynamics
Yazhou Chen, Dehua Wang and Rongfang Zhang
2021, 29(6) : 3817-3832 doi: 10.3934/era.2021063 +[Abstract](377) +[HTML](192) +[PDF](353.68KB)
Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations
Yang Cao and Qiuting Zhao
2021, 29(6) : 3833-3851 doi: 10.3934/era.2021064 +[Abstract](289) +[HTML](151) +[PDF](378.74KB)
A computable formula for the class number of the imaginary quadratic field $ \mathbb Q(\sqrt{-p}), \ p = 4n-1 $
Jorge Garcia Villeda
2021, 29(6) : 3853-3865 doi: 10.3934/era.2021065 +[Abstract](392) +[HTML](148) +[PDF](321.17KB)
A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms
Yi Cheng and Ying Chu
2021, 29(6) : 3867-3887 doi: 10.3934/era.2021066 +[Abstract](393) +[HTML](153) +[PDF](413.81KB)
Optimal time-decay rates of the compressible Navier–Stokes–Poisson system in $ \mathbb R^3 $
Guochun Wu, Han Wang and Yinghui Zhang
2021, 29(6) : 3889-3908 doi: 10.3934/era.2021067 +[Abstract](352) +[HTML](173) +[PDF](388.28KB)
The algebraic classification of nilpotent commutative algebras
Doston Jumaniyozov, Ivan Kaygorodov and Abror Khudoyberdiyev
2021, 29(6) : 3909-3993 doi: 10.3934/era.2021068 +[Abstract](338) +[HTML](146) +[PDF](665.92KB)
Variations on Lyapunov's stability criterion and periodic prey-predator systems
Rafael Ortega
2021, 29(6) : 3995-4008 doi: 10.3934/era.2021069 +[Abstract](330) +[HTML](162) +[PDF](334.88KB)
Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow
Long Fan, Cheng-Jie Liu and Lizhi Ruan
2021, 29(6) : 4009-4050 doi: 10.3934/era.2021070 +[Abstract](330) +[HTML](146) +[PDF](501.24KB)
Stabilizing effect of elasticity on the motion of viscoelastic/elastic fluids
Fei Jiang
2021, 29(6) : 4051-4074 doi: 10.3934/era.2021071 +[Abstract](324) +[HTML](144) +[PDF](414.7KB)
Nonexistence of entire positive solutions for conformal Hessian quotient inequalities
Feida Jiang, Xi Chen and Juhua Shi
2021, 29(6) : 4075-4086 doi: 10.3934/era.2021072 +[Abstract](272) +[HTML](115) +[PDF](328.43KB)
Non-global solution for visco-elastic dynamical system with nonlinear source term in control problem
Xiaoqiang Dai and Wenke Li
2021, 29(6) : 4087-4098 doi: 10.3934/era.2021073 +[Abstract](230) +[HTML](110) +[PDF](320.73KB)
Some estimates of virtual element methods for fourth order problems
Qingguang Guan
2021, 29(6) : 4099-4118 doi: 10.3934/era.2021074 +[Abstract](257) +[HTML](119) +[PDF](354.25KB)
Accelerating reinforcement learning with a Directional-Gaussian-Smoothing evolution strategy
Jiaxin Zhang, Hoang Tran and Guannan Zhang
2021, 29(6) : 4119-4135 doi: 10.3934/era.2021075 +[Abstract](312) +[HTML](119) +[PDF](2281.58KB)
Pullback dynamics of a 3D modified Navier-Stokes equations with double delays
Pan Zhang, Lan Huang, Rui Lu and Xin-Guang Yang
2021, 29(6) : 4137-4157 doi: 10.3934/era.2021076 +[Abstract](196) +[HTML](94) +[PDF](392.68KB)
Global dynamics of some system of second-order difference equations
Tran Hong Thai, Nguyen Anh Dai and Pham Tuan Anh
2021, 29(6) : 4159-4175 doi: 10.3934/era.2021077 +[Abstract](221) +[HTML](116) +[PDF](664.58KB)
On the existence of solutions for the Frenkel-Kontorova models on quasi-crystals
Jianxing Du and Xifeng Su
2021, 29(6) : 4177-4198 doi: 10.3934/era.2021078 +[Abstract](197) +[HTML](91) +[PDF](685.78KB)
Path-connectedness in global bifurcation theory
J. F. Toland
2021, 29(6) : 4199-4213 doi: 10.3934/era.2021079 +[Abstract](199) +[HTML](84) +[PDF](359.03KB)
On the number of critical points of solutions of semilinear elliptic equations
Massimo Grossi
2021, 29(6) : 4215-4228 doi: 10.3934/era.2021080 +[Abstract](215) +[HTML](117) +[PDF](918.14KB)
Planar vortices in a bounded domain with a hole
Shusen Yan and Weilin Yu
2021, 29(6) : 4229-4241 doi: 10.3934/era.2021081 +[Abstract](199) +[HTML](104) +[PDF](386.58KB)
Well-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity
Wei-Xi Li and Rui Xu
2021, 29(6) : 4243-4255 doi: 10.3934/era.2021082 +[Abstract](215) +[HTML](103) +[PDF](368.62KB)
Congruences for sixth order mock theta functions $ \lambda(q) $ and $ \rho(q) $
Harman Kaur and Meenakshi Rana
2021, 29(6) : 4257-4268 doi: 10.3934/era.2021084 +[Abstract](186) +[HTML](51) +[PDF](301.81KB)
Optimal control for the coupled chemotaxis-fluid models in two space dimensions
Yunfei Yuan and Changchun Liu
2021, 29(6) : 4269-4296 doi: 10.3934/era.2021085 +[Abstract](220) +[HTML](79) +[PDF](389.03KB)
Global dynamics in a competitive two-species and two-stimuli chemotaxis system with chemical signalling loop
Rong Zhang and Liangchen Wang
2021, 29(6) : 4297-4314 doi: 10.3934/era.2021086 +[Abstract](152) +[HTML](95) +[PDF](425.7KB)
Canonical maps of general hypersurfaces in Abelian varieties
Fabrizio Catanese and Luca Cesarano
2021, 29(6) : 4315-4325 doi: 10.3934/era.2021087 +[Abstract](183) +[HTML](55) +[PDF](342.07KB)
Yamabe systems and optimal partitions on manifolds with symmetries
Mónica Clapp and Angela Pistoia
2021, 29(6) : 4327-4338 doi: 10.3934/era.2021088 +[Abstract](165) +[HTML](52) +[PDF](393.98KB)
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](1425) +[HTML](668) +[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](1142) +[HTML](591) +[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](1335) +[HTML](538) +[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](2194) +[HTML](1029) +[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](1080) +[HTML](645) +[PDF](3941.13KB) Cited By(2)
Global existence and energy decay of solutions for a wave equation with non-constant delay and nonlinear weights
Vanessa Barros, Carlos Nonato and Carlos Raposo
2020, 28: 205-220 doi: 10.3934/era.2020014 +[Abstract](1505) +[HTML](570) +[PDF](347.49KB) 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](1229) +[HTML](582) +[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](1998) +[HTML](933) +[PDF](448.4KB) Cited By(2)
Some multivariate polynomials for doubled permutations
Bin Han
2021, 29: 1925-1944 doi: 10.3934/era.2020098 +[Abstract](1144) +[HTML](575) +[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](1202) +[HTML](620) +[PDF](492.02KB) Cited By(2)
A survey of gradient methods for solving nonlinear optimization
Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma and Dijana Mosić
2020, 28: 1573-1624 doi: 10.3934/era.2020115 +[Abstract](1658) +[HTML](653) +[PDF](716.69KB) PDF Downloads(511)
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](2514) +[HTML](1091) +[PDF](313.13KB) PDF Downloads(466)
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](1864) +[HTML](558) +[PDF](484.76KB) PDF Downloads(458)
Some properties for almost cellular algebras
Yongjie Wang and Nan Gao
2021, 29: 1681-1689 doi: 10.3934/era.2020086 +[Abstract](1037) +[HTML](461) +[PDF](297.34KB) PDF Downloads(425)
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](1618) +[HTML](662) +[PDF](383.54KB) PDF Downloads(403)
A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations
Guoliang Zhang, Shaoqin Zheng and Tao Xiong
2021, 29: 1819-1839 doi: 10.3934/era.2020093 +[Abstract](1334) +[HTML](623) +[PDF](522.1KB) PDF Downloads(396)
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](1855) +[HTML](864) +[PDF](369.78KB) PDF Downloads(390)
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](1425) +[HTML](668) +[PDF](392.76KB) PDF Downloads(375)
$ 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](1357) +[HTML](834) +[PDF](392.34KB) PDF Downloads(373)
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](1290) +[HTML](577) +[PDF](5508.22KB) PDF Downloads(367)

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