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Discrete & Continuous Dynamical Systems (DCDS) publishes peer-reviewed original and expository papers on the theory, methods and applications of analysis, differential equations and dynamical systems. The journal is committed to recording important new methods and 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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Periodic and asymptotically periodic fourth-order Schrödinger equations with critical and subcritical growth
Edcarlos D. Silva, Marcos L. M. Carvalho and Claudiney Goulart
2022, 42(3) : 1039-1065 doi: 10.3934/dcds.2021146 +[Abstract](307) +[HTML](139) +[PDF](470.99KB)
Local well-posedness for the Zakharov system in dimension d ≤ 3
Akansha Sanwal
2022, 42(3) : 1067-1103 doi: 10.3934/dcds.2021147 +[Abstract](355) +[HTML](151) +[PDF](570.01KB)
Zero-dimensional and symbolic extensions of topological flows
David Burguet and Ruxi Shi
2022, 42(3) : 1105-1126 doi: 10.3934/dcds.2021148 +[Abstract](257) +[HTML](134) +[PDF](502.68KB)
Two species nonlocal diffusion systems with free boundaries
Yihong Du, Mingxin Wang and Meng Zhao
2022, 42(3) : 1127-1162 doi: 10.3934/dcds.2021149 +[Abstract](444) +[HTML](199) +[PDF](485.18KB)
Topological mild mixing of all orders along polynomials
Yang Cao and Song Shao
2022, 42(3) : 1163-1184 doi: 10.3934/dcds.2021150 +[Abstract](216) +[HTML](114) +[PDF](449.04KB)
Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains
Alessio Falocchi and Filippo Gazzola
2022, 42(3) : 1185-1200 doi: 10.3934/dcds.2021151 +[Abstract](237) +[HTML](105) +[PDF](1188.63KB)
Global $ C^2 $-estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition
Zhenghuan Gao and Peihe Wang
2022, 42(3) : 1201-1223 doi: 10.3934/dcds.2021152 +[Abstract](247) +[HTML](104) +[PDF](395.8KB)
Statistics of multipliers for hyperbolic rational maps
Richard Sharp and Anastasios Stylianou
2022, 42(3) : 1225-1241 doi: 10.3934/dcds.2021153 +[Abstract](260) +[HTML](117) +[PDF](390.69KB)
Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory
Guangcun Lu
2022, 42(3) : 1243-1316 doi: 10.3934/dcds.2021154 +[Abstract](262) +[HTML](151) +[PDF](807.43KB)
Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems
Guangcun Lu
2022, 42(3) : 1317-1368 doi: 10.3934/dcds.2021155 +[Abstract](247) +[HTML](116) +[PDF](684.27KB)
Elliptic systems involving Schrödinger operators with vanishing potentials
Juan Arratia, Denilson Pereira and Pedro Ubilla
2022, 42(3) : 1369-1401 doi: 10.3934/dcds.2021156 +[Abstract](267) +[HTML](131) +[PDF](845.27KB)
Number of bounded distance equivalence classes in hulls of repetitive Delone sets
Dirk Frettlöh, Alexey Garber and Lorenzo Sadun
2022, 42(3) : 1403-1414 doi: 10.3934/dcds.2021157 +[Abstract](222) +[HTML](106) +[PDF](329.58KB)
Lower bounds for Orlicz eigenvalues
Ariel Salort
2022, 42(3) : 1415-1434 doi: 10.3934/dcds.2021158 +[Abstract](223) +[HTML](110) +[PDF](390.58KB)
On the structure of $ \alpha $-limit sets of backward trajectories for graph maps
Magdalena Foryś-Krawiec, Jana Hantáková and Piotr Oprocha
2022, 42(3) : 1435-1463 doi: 10.3934/dcds.2021159 +[Abstract](256) +[HTML](121) +[PDF](527.93KB)
Eternal solutions for a reaction-diffusion equation with weighted reaction
Razvan Gabriel Iagar and Ariel Sánchez
2022, 42(3) : 1465-1491 doi: 10.3934/dcds.2021160 +[Abstract](311) +[HTML](111) +[PDF](661.43KB)
An Erratum on "Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay" (Discrete Continuous Dynamic Systems, 40(3), 2020, 1493-1515)
Xin-Guang Yang
2022, 42(3) : 1493-1494 doi: 10.3934/dcds.2021161 +[Abstract](242) +[HTML](116) +[PDF](167.8KB)
Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles
Kai Tao
2022, 42(3) : 1495-1533 doi: 10.3934/dcds.2021162 +[Abstract](207) +[HTML](107) +[PDF](508.13KB)
On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model
Chaoying Li, Xiaojing Xu and Zhuan Ye
2022, 42(3) : 1535-1568 doi: 10.3934/dcds.2021163 +[Abstract](199) +[HTML](98) +[PDF](428.76KB)
Quantitative destruction of invariant circles
Lin Wang
2022, 42(3) : 1569-1583 doi: 10.3934/dcds.2021164 +[Abstract](181) +[HTML](86) +[PDF](345.88KB)
Expansive flows on uniform spaces
Se-Hyun Ku
2022, 42(3) : 1585-1598 doi: 10.3934/dcds.2021165 +[Abstract](238) +[HTML](111) +[PDF](344.15KB)
Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay
Ning Wang and Zhi-Cheng Wang
2021doi: 10.3934/dcds.2021166 +[Abstract](227) +[HTML](112) +[PDF](2777.52KB)
Stability of optimal traffic plans in the irrigation problem
Maria Colombo, Antonio De Rosa, Andrea Marchese, Paul Pegon and Antoine Prouff
2021doi: 10.3934/dcds.2021167 +[Abstract](276) +[HTML](118) +[PDF](375.25KB)
Rigidity, weak mixing, and recurrence in abelian groups
Ethan M. Ackelsberg
2021doi: 10.3934/dcds.2021168 +[Abstract](220) +[HTML](102) +[PDF](514.34KB)
On super-exponential divergence of periodic points for partially hyperbolic systems
Xiaolong Li and Katsutoshi Shinohara
2021doi: 10.3934/dcds.2021169 +[Abstract](211) +[HTML](96) +[PDF](412.02KB)
Nonlinear nonlocal reaction-diffusion problem with local reaction
Aníbal Rodríguez-Bernal and Silvia Sastre-Gómez
2021doi: 10.3934/dcds.2021170 +[Abstract](223) +[HTML](105) +[PDF](500.06KB)
Instability of the soliton for the focusing, mass-critical generalized KdV equation
Benjamin Dodson and Cristian Gavrus
2021doi: 10.3934/dcds.2021171 +[Abstract](176) +[HTML](100) +[PDF](487.6KB)
Multiplicity of closed Reeb orbits on dynamically convex $ \mathbb{R}P^{2n-1} $ for $ n\geq2 $
Hui Liu and Ling Zhang
2021doi: 10.3934/dcds.2021172 +[Abstract](233) +[HTML](95) +[PDF](389.67KB)
Fujita type results for quasilinear parabolic inequalities with nonlocal terms
Roberta Filippucci and Marius Ghergu
2021doi: 10.3934/dcds.2021173 +[Abstract](202) +[HTML](99) +[PDF](358.71KB)
On $ L^1 $ estimates of solutions of compressible viscoelastic system
Yusuke Ishigaki
2021doi: 10.3934/dcds.2021174 +[Abstract](173) +[HTML](91) +[PDF](181.31KB)
Sublacunary sets and interpolation sets for nilsequences
Anh N. Le
2021doi: 10.3934/dcds.2021175 +[Abstract](200) +[HTML](86) +[PDF](356.98KB)
Random attractors for dissipative systems with rough noises
Luu Hoang Duc
2021doi: 10.3934/dcds.2021176 +[Abstract](224) +[HTML](224) +[PDF](441.23KB)
Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions
Corentin Le Bihan
2021doi: 10.3934/dcds.2021177 +[Abstract](180) +[HTML](92) +[PDF](566.6KB)
A symmetric property in the enhanced common index jump theorem with applications to the closed geodesic problem
Muhammad Hamid and Wei Wang
2021doi: 10.3934/dcds.2021178 +[Abstract](180) +[HTML](98) +[PDF](367.98KB)
Global propagation of singularities for discounted Hamilton-Jacobi equations
Cui Chen, Jiahui Hong and Kai Zhao
2021doi: 10.3934/dcds.2021179 +[Abstract](182) +[HTML](95) +[PDF](396.93KB)
High and low perturbations of Choquard equations with critical reaction and variable growth
Youpei Zhang, Xianhua Tang and Vicenţiu D. Rădulescu
2021doi: 10.3934/dcds.2021180 +[Abstract](205) +[HTML](91) +[PDF](475.49KB)
Existence of minimizers for one-dimensional vectorial non-semicontinuous functionals with second order lagrangian
Sandro Zagatti
2021doi: 10.3934/dcds.2021181 +[Abstract](232) +[HTML](94) +[PDF](360.96KB)
Crystalline flow starting from a general polygon
Mi-Ho Giga, Yoshikazu Giga, Ryo Kuroda and Yusuke Ochiai
2021doi: 10.3934/dcds.2021182 +[Abstract](219) +[HTML](86) +[PDF](536.0KB)
Equidistribution of translates of a homogeneous measure on the Borel–Serre compactification
Runlin Zhang
2021doi: 10.3934/dcds.2021183 +[Abstract](239) +[HTML](87) +[PDF](428.33KB)
Liouville-type theorem for high order degenerate Lane-Emden system
Yuxia Guo and Ting Liu
2021doi: 10.3934/dcds.2021184 +[Abstract](199) +[HTML](84) +[PDF](440.63KB)
Geodesic planes in geometrically finite manifolds-corrigendum
Osama Khalil
2021doi: 10.3934/dcds.2021185 +[Abstract](288) +[HTML](71) +[PDF](147.87KB)
Lifting the regionally proximal relation and characterizations of distal extensions
Kai Cao and Xiongping Dai
2021doi: 10.3934/dcds.2021186 +[Abstract](216) +[HTML](75) +[PDF](862.1KB)
Global weak solutions to the stochastic Ericksen–Leslie system in dimension two
Hengrong Du and Changyou Wang
2021doi: 10.3934/dcds.2021187 +[Abstract](110) +[HTML](53) +[PDF](371.0KB)
Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains
Nam Q. Le
2021doi: 10.3934/dcds.2021188 +[Abstract](105) +[HTML](52) +[PDF](332.14KB)
A dissipative logarithmic-Laplacian type of plate equation: Asymptotic profile and decay rates
Ruy Coimbra Charão, Alessandra Piske and Ryo Ikehata
2021doi: 10.3934/dcds.2021189 +[Abstract](180) +[HTML](60) +[PDF](506.48KB)
On the Cauchy problems associated to a ZK-KP-type family equations with a transversal fractional dispersion
Jorge Morales Paredes and Félix Humberto Soriano Méndez
2021doi: 10.3934/dcds.2021190 +[Abstract](124) +[HTML](53) +[PDF](483.4KB)
Refinements of topological invariants of flows
Tomoo Yokoyama
2021doi: 10.3934/dcds.2021191 +[Abstract](141) +[HTML](60) +[PDF](976.72KB)
One component regularity criteria for the axially symmetric MHD-Boussinesq system
Zijin Li and Xinghong Pan
2021doi: 10.3934/dcds.2021192 +[Abstract](110) +[HTML](49) +[PDF](443.43KB)
"Large" strange attractors in the unfolding of a heteroclinic attractor
Alexandre Rodrigues
2021doi: 10.3934/dcds.2021193 +[Abstract](107) +[HTML](53) +[PDF](497.49KB)
Self polarization and traveling wave in a model for cell crawling migration
Alessandro Cucchi, Antoine Mellet and Nicolas Meunier
2021doi: 10.3934/dcds.2021194 +[Abstract](91) +[HTML](48) +[PDF](447.85KB)
Cucker-Smale model with time delay
Mauro Rodriguez Cartabia
2021doi: 10.3934/dcds.2021195 +[Abstract](124) +[HTML](51) +[PDF](1942.73KB)
Erratum and addendum to "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" (Volume 40, Number 4, 2020, 2285-2313)
Shuhei Hayashi
2021doi: 10.3934/dcds.2021196 +[Abstract](182) +[HTML](45) +[PDF](248.05KB)
Shadowing as a structural property of the space of dynamical systems
Jonathan Meddaugh
2021doi: 10.3934/dcds.2021197 +[Abstract](122) +[HTML](49) +[PDF](267.29KB)
A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials
Dong Li
2022doi: 10.3934/dcds.2021198 +[Abstract](77) +[HTML](38) +[PDF](254.83KB)
On the multifractal spectrum of weighted Birkhoff averages
Balázs Bárány, Michaƚ Rams and Ruxi Shi
2022doi: 10.3934/dcds.2021199 +[Abstract](88) +[HTML](32) +[PDF](595.23KB)
Stability, free energy and dynamics of multi-spikes in the minimal Keller-Segel model
Fanze Kong and Qi Wang
2022doi: 10.3934/dcds.2021200 +[Abstract](98) +[HTML](45) +[PDF](4424.72KB)
On the density of certain spectral points for a class of $ C^{2} $ quasiperiodic Schrödinger cocycles
Fan Wu, Linlin Fu and Jiahao Xu
2022doi: 10.3934/dcds.2021201 +[Abstract](92) +[HTML](37) +[PDF](408.83KB)
Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields
Jeongho Kim and Bora Moon
2022doi: 10.3934/dcds.2021202 +[Abstract](83) +[HTML](36) +[PDF](406.76KB)
On the one dimensional cubic NLS in a critical space
Marco Bravin and Luis Vega
2022doi: 10.3934/dcds.2021203 +[Abstract](74) +[HTML](31) +[PDF](383.49KB)
Higher dimensional topology and generalized Hopf bifurcations for discrete dynamical systems
Héctor Barge and José M. R. Sanjurjo
2022doi: 10.3934/dcds.2021204 +[Abstract](97) +[HTML](53) +[PDF](325.89KB)
Pointwise estimates of the solution to one dimensional compressible Naiver-Stokes equations in half space
Hailiang Li, Houzhi Tang and Haitao Wang
2022doi: 10.3934/dcds.2021205 +[Abstract](94) +[HTML](33) +[PDF](418.69KB)
Global well-posedness for fractional Sobolev-Galpern type equations
Huy Tuan Nguyen, Nguyen Anh Tuan and Chao Yang
2022doi: 10.3934/dcds.2021206 +[Abstract](76) +[HTML](33) +[PDF](478.21KB)
Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains
Teo Kukuljan
2022doi: 10.3934/dcds.2021207 +[Abstract](76) +[HTML](35) +[PDF](467.33KB)
On involution kernels and large deviations principles on $ \beta $-shifts
Victor Vargas
2022doi: 10.3934/dcds.2021208 +[Abstract](74) +[HTML](32) +[PDF](441.88KB)
A free boundary problem of nonlinear diffusion equation with positive bistable nonlinearity in high space dimensions I : Classification of asymptotic behavior
Yuki Kaneko, Hiroshi Matsuzawa and Yoshio Yamada
2022doi: 10.3934/dcds.2021209 +[Abstract](171) +[HTML](36) +[PDF](415.18KB)
Perturbative Cauchy theory for a flux-incompressible Maxwell-Stefan system
Andrea Bondesan and Marc Briant
2022doi: 10.3934/dcds.2021210 +[Abstract](67) +[HTML](24) +[PDF](622.67KB)
On $ n $-tuplewise IP-sensitivity and thick sensitivity
Jian Li and Yini Yang
2022doi: 10.3934/dcds.2021211 +[Abstract](97) +[HTML](30) +[PDF](455.14KB)
Stability of hyperbolic Oseledets splittings for quasi-compact operator cocycles
Harry Crimmins
2022doi: 10.3934/dcds.2022001 +[Abstract](63) +[HTML](20) +[PDF](731.82KB)
The primitive equations of the polluted atmosphere as a weak and strong limit of the 3D Navier-Stokes equations in downwind-matching coordinates
Donatella Donatelli and Nóra Juhász
2022doi: 10.3934/dcds.2022002 +[Abstract](65) +[HTML](28) +[PDF](498.51KB)
Persistence and convergence in parabolic-parabolic chemotaxis system with logistic source on $ \mathbb{R}^{N} $
Wenxian Shen and Shuwen Xue
2022doi: 10.3934/dcds.2022003 +[Abstract](71) +[HTML](40) +[PDF](496.63KB)
Global regularity for the 3D compressible magnetohydrodynamics with general pressure
Anthony Suen
2022doi: 10.3934/dcds.2022004 +[Abstract](58) +[HTML](19) +[PDF](354.7KB)
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](9294) +[PDF](382.7KB) Cited By(319)
Variational methods for non-local operators of elliptic type
Raffaella Servadei and Enrico Valdinoci
2013, 33(5) : 2105-2137 doi: 10.3934/dcds.2013.33.2105 +[Abstract](6169) +[PDF](418.8KB) Cited By(292)
Global well-posedness of the viscous Boussinesq equations
Thomas Y. Hou and Congming Li
2005, 12(1) : 1-12 doi: 10.3934/dcds.2005.12.1 +[Abstract](4679) +[PDF](203.5KB) Cited By(209)
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](8313) +[PDF](262.8KB) Cited By(202)
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](6031) +[PDF](233.8KB) Cited By(202)
Global attractors for damped semilinear wave equations
John M. Ball
2004, 10(1&2) : 31-52 doi: 10.3934/dcds.2004.10.31 +[Abstract](7434) +[PDF](246.2KB) Cited By(198)
Partial regularity of the dynamic system modeling the flow of liquid crystals
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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](6833) +[PDF](369.4KB) Cited By(169)
Remarks on regularities for the 3D MHD equations
Yong Zhou
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
Linda J. S. Allen, B. M. Bolker, Yuan Lou and A. L. Nevai
2008, 21(1) : 1-20 doi: 10.3934/dcds.2008.21.1 +[Abstract](8756) +[PDF](401.1KB) Cited By(155)
The problem Of blow-up in nonlinear parabolic equations
Victor A. Galaktionov and Juan-Luis Vázquez
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Some questions looking for answers in dynamical systems
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2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](6018) +[HTML](369) +[PDF](531.03KB) PDF Downloads(1900)
The vorticity equation on a rotating sphere and the shallow fluid approximation
Vikas S. Krishnamurthy
2019, 39(11) : 6261-6276 doi: 10.3934/dcds.2019273 +[Abstract](2139) +[HTML](168) +[PDF](370.02KB) PDF Downloads(1587)
Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
David Simmons
2012, 32(7) : 2565-2582 doi: 10.3934/dcds.2012.32.2565 +[Abstract](4076) +[PDF](444.9KB) PDF Downloads(1371)
Differentiability of the Hartman--Grobman linearization
Misha Guysinsky, Boris Hasselblatt and Victoria Rayskin
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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](9294) +[PDF](382.7KB) PDF Downloads(952)
Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
Linda J. S. Allen, B. M. Bolker, Yuan Lou and A. L. Nevai
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On the spectral theory of positive operators and PDE applications
Kung-Ching Chang, Xuefeng Wang and Xie Wu
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Understanding Thomas-Fermi-Like approximations: Averaging over oscillating occupied orbitals
John P. Perdew and Adrienn Ruzsinszky
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On Geometric Mechanics
Jean-Marie Souriau
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