American Institute of Mathematical Sciences

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AIMS joins the mathematics community worldwide in congratulating ProfessorAlessio Figalli on being awarded the Fields Medal 2018. Professor Figallihas made important contributions to AIMS journals and conferences. Heserved as the Managing Editor of Discrete and Continuous Dynamical Systemsfrom 2012 to 2016 and delivered a plenary lecture at the 11th AIMSconference (2016) in Orlando, USA. Details can be found at http://aimsciences.org/conferences/2016/2016_speakers.html

Congratulations, Alessio!

DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.

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Stationary states of the cubic conformal flow on $ \mathbb{S}^3 $

Piotr Bizoń, Dominika Hunik-Kostyra and Dmitry Pelinovsky

2020, 40(1) : 1-32 doi: 10.3934/dcds.2020001 +[Abstract](147) +[HTML](49) +[PDF](572.12KB)

Hereditarily non uniformly perfect non-autonomous Julia sets

Mark Comerford, Rich Stankewitz and Hiroki Sumi

2020, 40(1) : 33-46 doi: 10.3934/dcds.2020002 +[Abstract](132) +[HTML](50) +[PDF](7082.74KB)

Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line

Razvan Mosincat and Haewon Yoon

2020, 40(1) : 47-80 doi: 10.3934/dcds.2020003 +[Abstract](130) +[HTML](62) +[PDF](581.28KB)

Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems

Xinsheng Wang, Weisheng Wu and Yujun Zhu

2020, 40(1) : 81-105 doi: 10.3934/dcds.2020004 +[Abstract](116) +[HTML](46) +[PDF](404.02KB)

Regularity of extremal solutions of nonlocal elliptic systems

Mostafa Fazly

2020, 40(1) : 107-131 doi: 10.3934/dcds.2020005 +[Abstract](112) +[HTML](45) +[PDF](456.82KB)

Non-potential and non-radial Dirichlet systems with mean curvature operator in Minkowski space

Daniela Gurban, Petru Jebelean and Cǎlin Şerban

2020, 40(1) : 133-151 doi: 10.3934/dcds.2020006 +[Abstract](158) +[HTML](47) +[PDF](385.42KB)

Discrete N-barrier maximum principle for a lattice dynamical system arising in competition models

Chiun-Chuan Chen, Ting-Yang Hsiao and Li-Chang Hung

2020, 40(1) : 153-187 doi: 10.3934/dcds.2020007 +[Abstract](119) +[HTML](52) +[PDF](369.27KB)

Singularities of certain finite energy solutions to the Navier-Stokes system

Grzegorz Karch, Maria E. Schonbek and Tomas P. Schonbek

2020, 40(1) : 189-206 doi: 10.3934/dcds.2020008 +[Abstract](116) +[HTML](50) +[PDF](381.62KB)

A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors

Marianne Akian, Stéphane Gaubert and Antoine Hochart

2020, 40(1) : 207-231 doi: 10.3934/dcds.2020009 +[Abstract](156) +[HTML](53) +[PDF](434.38KB)

Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux

Marco Di Francesco and Graziano Stivaletta

2020, 40(1) : 233-266 doi: 10.3934/dcds.2020010 +[Abstract](121) +[HTML](55) +[PDF](432.07KB)

Almost sure global well posedness for the BBM equation with infinite $ L^{2} $ initial data

Justin Forlano

2020, 40(1) : 267-318 doi: 10.3934/dcds.2020011 +[Abstract](140) +[HTML](76) +[PDF](626.09KB)

A shift map with a discontinuous entropy function

Christian Wolf

2020, 40(1) : 319-329 doi: 10.3934/dcds.2020012 +[Abstract](123) +[HTML](47) +[PDF](348.08KB)

Fermi's golden rule and $ H^1 $ scattering for nonlinear Klein-Gordon equations with metastable states

Xinliang An and Avy Soffer

2020, 40(1) : 331-373 doi: 10.3934/dcds.2020013 +[Abstract](102) +[HTML](55) +[PDF](517.57KB)

Interpolation inequalities in $ \mathrm W^{1,p}( {\mathbb S}^1) $ and carré du champ methods

Jean Dolbeault, Marta García-Huidobro and Rául Manásevich

2020, 40(1) : 375-394 doi: 10.3934/dcds.2020014 +[Abstract](122) +[HTML](44) +[PDF](474.13KB)

Derivation of geostrophic equations as a rigorous limit of compressible rotating and heat conducting fluids with the general initial data

Young-Sam Kwon and Antonin Novotny

2020, 40(1) : 395-421 doi: 10.3934/dcds.2020015 +[Abstract](105) +[HTML](46) +[PDF](679.78KB)

On the radius of spatial analyticity for defocusing nonlinear Schrödinger equations

Jaeseop Ahn, Jimyeong Kim and Ihyeok Seo

2020, 40(1) : 423-439 doi: 10.3934/dcds.2020016 +[Abstract](102) +[HTML](49) +[PDF](371.21KB)

Anosov diffeomorphism with a horseshoe that attracts almost any point

Christian Bonatti, Stanislav Minkov, Alexey Okunev and Ivan Shilin

2020, 40(1) : 441-465 doi: 10.3934/dcds.2020017 +[Abstract](126) +[HTML](50) +[PDF](553.15KB)

Existence of positive solutions for integral systems of the weighted Hardy-Littlewood-Sobolev type

Xiaoqian Liu and Yutian Lei

2020, 40(1) : 467-489 doi: 10.3934/dcds.2020018 +[Abstract](130) +[HTML](58) +[PDF](378.26KB)

Variational principles of invariance pressures on partitions

Xing-Fu Zhong

2020, 40(1) : 491-508 doi: 10.3934/dcds.2020019 +[Abstract](123) +[HTML](43) +[PDF](358.76KB)

Discrete maximal regularity for volterra equations and nonlocal time-stepping schemes

Carlos Lizama and Marina Murillo-Arcila

2020, 40(1) : 509-528 doi: 10.3934/dcds.2020020 +[Abstract](116) +[HTML](54) +[PDF](387.21KB)

Compacton equations and integrability: The rosenau-hyman and Cooper-Shepard-Sodano equations

Rafael Hernández Heredero, Marianna Euler, Norbert Euler and Enrique G. Reyes

2020, 40(1) : 529-548 doi: 10.3934/dcds.2020021 +[Abstract](79) +[HTML](45) +[PDF](381.9KB)

Symmetry and monotonicity properties of singular solutions to some cooperative semilinear elliptic systems involving critical nonlinearities

Francesco Esposito

2020, 40(1) : 549-577 doi: 10.3934/dcds.2020022 +[Abstract](103) +[HTML](55) +[PDF](414.22KB)

Existence and nonexistence of subsolutions for augmented Hessian equations

Limei Dai

2020, 40(1) : 579-596 doi: 10.3934/dcds.2020023 +[Abstract](105) +[HTML](44) +[PDF](363.97KB)

Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

Hyeongjin Lee, Ihyeok Seo and Jihyeon Seok

2020, 40(1) : 597-608 doi: 10.3934/dcds.2020024 +[Abstract](112) +[HTML](49) +[PDF](331.49KB)

Global stability of Keller–Segel systems in critical Lebesgue spaces

Jie Jiang

2020, 40(1) : 609-634 doi: 10.3934/dcds.2020025 +[Abstract](119) +[HTML](46) +[PDF](460.81KB)

Traveling waves for some nonlocal 1D Gross–Pitaevskii equations with nonzero conditions at infinity

André de Laire and Pierre Mennuni

2020, 40(1) : 635-682 doi: 10.3934/dcds.2020026 +[Abstract](120) +[HTML](53) +[PDF](919.16KB)

A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation

Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura and Tohru Wakasa

2019doi: 10.3934/dcds.2019226 +[Abstract](797) +[HTML](278) +[PDF](479.3KB)

Cauchy problem of semilinear inhomogeneous elliptic equations of Matukuma-type with multiple growth terms

Yunfeng Jia, Yi Li, Jianhua Wu and Hong-Kun Xu

2019doi: 10.3934/dcds.2019227 +[Abstract](595) +[HTML](247) +[PDF](399.3KB)

Nondegeneracy of harmonic maps from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $

Guoyuan Chen, Yong Liu and Juncheng Wei

2019doi: 10.3934/dcds.2019228 +[Abstract](583) +[HTML](236) +[PDF](370.56KB)

Large time behavior of ODE type solutions to nonlinear diffusion equations

Junyong Eom and Kazuhiro Ishige

2019doi: 10.3934/dcds.2019229 +[Abstract](606) +[HTML](235) +[PDF](359.7KB)

Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature

Tianwen Luo, Tao Tao and Liqun Zhang

2019doi: 10.3934/dcds.2019230 +[Abstract](511) +[HTML](243) +[PDF](431.74KB)

Global stabilization of the full attraction-repulsion Keller-Segel system

Hai-Yang Jin and Zhi-An Wang

2019doi: 10.3934/dcds.2020027 +[Abstract](78) +[HTML](41) +[PDF](378.9KB)

A functional approach towards eigenvalue problems associated with incompressible flow

Shuang Liu and Yuan Lou

2019doi: 10.3934/dcds.2020028 +[Abstract](105) +[HTML](45) +[PDF](449.86KB)

On the viscous Camassa-Holm equations with fractional diffusion

Zaihui Gan, Fanghua Lin and Jiajun Tong

2019doi: 10.3934/dcds.2020029 +[Abstract](78) +[HTML](38) +[PDF](396.85KB)

Refined regularity and stabilization properties in a degenerate haptotaxis system

Michael Winkler and Christian Stinner

2019doi: 10.3934/dcds.2020030 +[Abstract](60) +[HTML](37) +[PDF](383.86KB)

Asymptotic population abundance of a two-patch system with asymmetric diffusion

Mengting Fang, Yuanshi Wang, Mingshu Chen and Donald L. DeAngelis

2019doi: 10.3934/dcds.2020031 +[Abstract](102) +[HTML](65) +[PDF](598.55KB)

Spectral asymptotics of radial solutions and nonradial bifurcation for the Hénon equation

Joel Kübler and Tobias Weth

2019doi: 10.3934/dcds.2020032 +[Abstract](88) +[HTML](43) +[PDF](474.43KB)

Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity

Maho Endo, Yuki Kaneko and Yoshio Yamada

2019doi: 10.3934/dcds.2020033 +[Abstract](132) +[HTML](61) +[PDF](203.66KB)

A Hopf lemma and regularity for fractional $ p $-Laplacians

Wenxiong Chen, Congming Li and Shijie Qi

2019doi: 10.3934/dcds.2020034 +[Abstract](76) +[HTML](35) +[PDF](386.0KB)

Global dynamics of competition models with nonsymmetric nonlocal dispersals when one diffusion rate is small

Xueli Bai and Fang Li

2019doi: 10.3934/dcds.2020035 +[Abstract](93) +[HTML](42) +[PDF](366.91KB)

Variational and operator methods for Maxwell-Stokes system

Xing-Bin Pan

2019doi: 10.3934/dcds.2020036 +[Abstract](83) +[HTML](58) +[PDF](542.41KB)

On space-time periodic solutions of the one-dimensional heat equation

Dong-Ho Tsai and Chia-Hsing Nien

2019doi: 10.3934/dcds.2020037 +[Abstract](78) +[HTML](32) +[PDF](426.74KB)

Simulation of post-hurricane impact on invasive species with biological control management

Linhao Xu, Marya Claire Zdechlik, Melissa C. Smith, Min B. Rayamajhi, Don L. DeAngelis and Bo Zhang

2019doi: 10.3934/dcds.2020038 +[Abstract](120) +[HTML](44) +[PDF](825.25KB)

Mean field equations on tori: Existence and uniqueness of evenly symmetric blow-up solutions

Daniele Bartolucci, Changfeng Gui, Yeyao Hu, Aleks Jevnikar and Wen Yang

2019doi: 10.3934/dcds.2020039 +[Abstract](59) +[HTML](33) +[PDF](458.42KB)

Eigenvalues of the Laplace-Beltrami operator under the homogeneous Neumann condition on a large zonal domain in the unit sphere

Yoshitsugu Kabeya

2019doi: 10.3934/dcds.2020040 +[Abstract](66) +[HTML](35) +[PDF](369.84KB)

Signed Radon measure-valued solutions of flux saturated scalar conservation laws

Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina and Alberto Tesei

2019doi: 10.3934/dcds.2020041 +[Abstract](77) +[HTML](39) +[PDF](479.51KB)

A stage structured model of delay differential equations for Aedes mosquito population suppression

Mugen Huang, Moxun Tang, Jianshe Yu and Bo Zheng

2019doi: 10.3934/dcds.2020042 +[Abstract](82) +[HTML](83) +[PDF](497.6KB)

Asymmetric dispersal and evolutional selection in two-patch system

Yong-Jung Kim, Hyowon Seo and Changwook Yoon

2019doi: 10.3934/dcds.2020043 +[Abstract](85) +[HTML](73) +[PDF](728.39KB)

Asymptotic homogenization for delay-differential equations and a question of analyticity

John Mallet-Paret and Roger D. Nussbaum

2019doi: 10.3934/dcds.2020044 +[Abstract](74) +[HTML](38) +[PDF](385.81KB)

Sectional symmetry of solutions of elliptic systems in cylindrical domains

Lucio Damascelli and Filomena Pacella

2019doi: 10.3934/dcds.2020045 +[Abstract](68) +[HTML](31) +[PDF](318.6KB)

Evolution equations involving nonlinear truncated Laplacian operators

Matthieu Alfaro and Isabeau Birindelli

2019doi: 10.3934/dcds.2020046 +[Abstract](64) +[HTML](43) +[PDF](361.4KB)

The sign of traveling wave speed in bistable dynamics

Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara and Chang-Hong Wu

2019doi: 10.3934/dcds.2020047 +[Abstract](87) +[HTML](55) +[PDF](308.89KB)

The impact of the domain boundary on an inhibitory system: Interior discs and boundary half discs

Xiaofeng Ren and David Shoup

2019doi: 10.3934/dcds.2020048 +[Abstract](73) +[HTML](26) +[PDF](586.41KB)

Spike solutions for a mass conservation reaction-diffusion system

Shin-Ichiro Ei and Shyuh-Yaur Tzeng

2019doi: 10.3934/dcds.2020049 +[Abstract](76) +[HTML](44) +[PDF](355.07KB)

Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach

Qian Liu, Shuang Liu and King-Yeung Lam

2019doi: 10.3934/dcds.2020050 +[Abstract](85) +[HTML](34) +[PDF](748.97KB)

Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion

Qing Li and Yaping Wu

2019doi: 10.3934/dcds.2020051 +[Abstract](77) +[HTML](36) +[PDF](676.08KB)

Type Ⅱ finite time blow-up for the energy critical heat equation in $ \mathbb{R}^4 $

Manuel del Pino, Monica Musso, Juncheng Wei and Yifu Zhou

2019doi: 10.3934/dcds.2020052 +[Abstract](76) +[HTML](65) +[PDF](484.25KB)

Bifurcation from infinity with applications to reaction-diffusion systems

Chihiro Aida, Chao-Nien Chen, Kousuke Kuto and Hirokazu Ninomiya

2019doi: 10.3934/dcds.2020053 +[Abstract](79) +[HTML](34) +[PDF](355.83KB)

On the spectral theory of positive operators and PDE applications

Kung-Ching Chang, Xuefeng Wang and Xie Wu

2019doi: 10.3934/dcds.2020054 +[Abstract](115) +[HTML](73) +[PDF](436.57KB)

Perturbative techniques for the construction of spike-layers

Andrea Malchiodi

2019doi: 10.3934/dcds.2020055 +[Abstract](65) +[HTML](70) +[PDF](373.27KB)

Monotone and nonmonotone clines with partial panmixia across a geographical barrier

Yantao Wang and Linlin Su

2019doi: 10.3934/dcds.2020056 +[Abstract](65) +[HTML](37) +[PDF](884.4KB)

Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation

Joachim Escher, Olaf Lechtenfeld and Zhaoyang Yin

2007, 19(3) : 493-513 doi: 10.3934/dcds.2007.19.493 +[Abstract](3665) +[PDF](233.8KB) ~~Cited By~~(162)

Global attractors for damped semilinear wave equations

John M. Ball

2004, 10(1&2) : 31-52 doi: 10.3934/dcds.2004.10.31 +[Abstract](4667) +[PDF](246.2KB) ~~Cited By~~(153)

Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

Xiaoyue Li and Xuerong Mao

2009, 24(2) : 523-545 doi: 10.3934/dcds.2009.24.523 +[Abstract](4556) +[PDF](262.8KB) ~~Cited By~~(142)

Remarks on regularities for the 3D MHD equations

Yong Zhou

2005, 12(5) : 881-886 doi: 10.3934/dcds.2005.12.881 +[Abstract](2545) +[PDF](176.3KB) ~~Cited By~~(141)

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

Jie Shen and Xiaofeng Yang

2010, 28(4) : 1669-1691 doi: 10.3934/dcds.2010.28.1669 +[Abstract](4139) +[PDF](382.7KB) ~~Cited By~~(133)

The problem Of blow-up in nonlinear parabolic equations

Victor A. Galaktionov and Juan-Luis Vázquez

2002, 8(2) : 399-433 doi: 10.3934/dcds.2002.8.399 +[Abstract](3591) +[PDF](369.4KB) ~~Cited By~~(113)

Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$

Zhengping Wang and Huan-Song Zhou

2007, 18(4) : 809-816 doi: 10.3934/dcds.2007.18.809 +[Abstract](2605) +[PDF](153.0KB) ~~Cited By~~(89)

BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity

Zhen Lei and Yi Zhou

2009, 25(2) : 575-583 doi: 10.3934/dcds.2009.25.575 +[Abstract](2673) +[PDF](159.5KB) ~~Cited By~~(82)

Global stability for damped Timoshenko systems

J.E. Muñoz Rivera and Reinhard Racke

2003, 9(6) : 1625-1639 doi: 10.3934/dcds.2003.9.1625 +[Abstract](2761) +[PDF](167.1KB) ~~Cited By~~(76)

Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces

Songsong Lu, Hongqing Wu and Chengkui Zhong

2005, 13(3) : 701-719 doi: 10.3934/dcds.2005.13.701 +[Abstract](2831) +[PDF](263.7KB) ~~Cited By~~(74)

Regularity and classification of solutions to static Hartree equations involving fractional Laplacians

Wei Dai, Jiahui Huang, Yu Qin, Bo Wang and Yanqin Fang

2019, 39(3) : 1389-1403 doi: 10.3934/dcds.2018117 +[Abstract](4063) +[HTML](779) +[PDF](472.85KB) ~~PDF Downloads~~(389)

Traveling wave solutions of a highly nonlinear shallow water equation

Anna Geyer and Ronald Quirchmayr

2018, 38(3) : 1567-1604 doi: 10.3934/dcds.2018065 +[Abstract](4833) +[HTML](2027) +[PDF](12373.99KB) ~~PDF Downloads~~(342)

On the universality of the incompressible Euler equation on compact manifolds

Terence Tao

2018, 38(3) : 1553-1565 doi: 10.3934/dcds.2018064 +[Abstract](3587) +[HTML](615) +[PDF](422.44KB) ~~PDF Downloads~~(250)

Some questions looking for answers in dynamical systems

Carles Simó

2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](2849) +[HTML](231) +[PDF](531.03KB) ~~PDF Downloads~~(235)

Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus

Ruofei Yao, Yi Li and Hongbin Chen

2019, 39(3) : 1585-1594 doi: 10.3934/dcds.2018122 +[Abstract](3754) +[HTML](629) +[PDF](388.54KB) ~~PDF Downloads~~(231)

On a class of non-local elliptic equations with asymptotically linear term

Yuanhong Wei and Xifeng Su

2018, 38(12) : 6287-6304 doi: 10.3934/dcds.2018154 +[Abstract](3270) +[HTML](489) +[PDF](442.05KB) ~~PDF Downloads~~(226)

Classification for positive solutions of degenerate elliptic system

Yuxia Guo and Jianjun Nie

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The two membranes problem for fully nonlinear operators

Luis Caffarelli, Luis Duque and Hernán Vivas

2018, 38(12) : 6015-6027 doi: 10.3934/dcds.2018152 +[Abstract](3112) +[HTML](391) +[PDF](364.45KB) ~~PDF Downloads~~(206)

Weakly mixing diffeomorphisms preserving a measurable Riemannian metric with prescribed Liouville rotation behavior

Roland Gunesch and Philipp Kunde

2018, 38(4) : 1615-1655 doi: 10.3934/dcds.2018067 +[Abstract](3567) +[HTML](451) +[PDF](683.82KB) ~~PDF Downloads~~(201)