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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

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
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Global attractors for damped semilinear wave equations
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Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
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Remarks on regularities for the 3D MHD equations
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
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The problem Of blow-up in nonlinear parabolic equations
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Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
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BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
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Global stability for damped Timoshenko systems
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Traveling wave solutions of a highly nonlinear shallow water equation
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Some questions looking for answers in dynamical systems
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Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
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The two membranes problem for fully nonlinear operators
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Weakly mixing diffeomorphisms preserving a measurable Riemannian metric with prescribed Liouville rotation behavior
Roland Gunesch and Philipp Kunde
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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
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