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Discrete & Continuous Dynamical Systems (DCDS) 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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Möbius disjointness for skew products on a circle and a nilmanifold
Wen Huang, Jianya Liu and Ke Wang
2021, 41(8) : 3531-3553 doi: 10.3934/dcds.2021006 +[Abstract](252) +[HTML](114) +[PDF](413.91KB)
Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative
Olivier Ley, Erwin Topp and Miguel Yangari
2021, 41(8) : 3555-3577 doi: 10.3934/dcds.2021007 +[Abstract](263) +[HTML](129) +[PDF](404.84KB)
Center stable manifolds around line solitary waves of the Zakharov–Kuznetsov equation with critical speed
Yohei Yamazaki
2021, 41(8) : 3579-3614 doi: 10.3934/dcds.2021008 +[Abstract](274) +[HTML](131) +[PDF](516.69KB)
On convergence to equilibria of flows of compressible viscous fluids under in/out–flux boundary conditions
Jan Březina, Eduard Feireisl and Antonín Novotný
2021, 41(8) : 3615-3627 doi: 10.3934/dcds.2021009 +[Abstract](232) +[HTML](126) +[PDF](392.64KB)
Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions
Sishu Shankar Muni, Robert I. McLachlan and David J. W. Simpson
2021, 41(8) : 3629-3650 doi: 10.3934/dcds.2021010 +[Abstract](525) +[HTML](150) +[PDF](2254.0KB)
The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function
Juntao Sun and Tsung-fang Wu
2021, 41(8) : 3651-3682 doi: 10.3934/dcds.2021011 +[Abstract](272) +[HTML](133) +[PDF](459.79KB)
A dynamical approach to lower and upper solutions for planar systems "To the memory of Massimo Tarallo"
Alessandro Fonda and Rodica Toader
2021, 41(8) : 3683-3708 doi: 10.3934/dcds.2021012 +[Abstract](277) +[HTML](124) +[PDF](417.71KB)
Proximality of multidimensional $ \mathscr{B} $-free systems
Aurelia Dymek
2021, 41(8) : 3709-3724 doi: 10.3934/dcds.2021013 +[Abstract](213) +[HTML](120) +[PDF](431.8KB)
Martin boundary of brownian motion on Gromov hyperbolic metric graphs
Soonki Hong and Seonhee Lim
2021, 41(8) : 3725-3757 doi: 10.3934/dcds.2021014 +[Abstract](258) +[HTML](118) +[PDF](637.74KB)
Stability of Broucke's isosceles orbit
Skyler Simmons
2021, 41(8) : 3759-3779 doi: 10.3934/dcds.2021015 +[Abstract](226) +[HTML](105) +[PDF](474.42KB)
Chaotic Delone sets
Jesús A. Álvarez López, Ramón Barral Lijó, John Hunton, Hiraku Nozawa and John R. Parker
2021, 41(8) : 3781-3796 doi: 10.3934/dcds.2021016 +[Abstract](253) +[HTML](110) +[PDF](916.42KB)
On fair entropy of the tent family
Bing Gao and Rui Gao
2021, 41(8) : 3797-3816 doi: 10.3934/dcds.2021017 +[Abstract](226) +[HTML](104) +[PDF](408.02KB)
Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five
Norman Noguera and Ademir Pastor
2021, 41(8) : 3817-3836 doi: 10.3934/dcds.2021018 +[Abstract](231) +[HTML](110) +[PDF](399.13KB)
On the splitting method for the nonlinear Schrödinger equation with initial data in $ H^1 $
Woocheol Choi and Youngwoo Koh
2021, 41(8) : 3837-3867 doi: 10.3934/dcds.2021019 +[Abstract](192) +[HTML](102) +[PDF](498.15KB)
Random substitution tilings and deviation phenomena
Scott Schmieding and Rodrigo Treviño
2021, 41(8) : 3869-3902 doi: 10.3934/dcds.2021020 +[Abstract](191) +[HTML](98) +[PDF](546.36KB)
On the cardinality of collisional clusters for hard spheres at low density
Mario Pulvirenti and Sergio Simonella
2021, 41(8) : 3903-3914 doi: 10.3934/dcds.2021021 +[Abstract](195) +[HTML](103) +[PDF](421.81KB)
A remark on the well-posedness of the modified KdV equation in the Fourier-Lebesgue spaces
Andreia Chapouto
2021, 41(8) : 3915-3950 doi: 10.3934/dcds.2021022 +[Abstract](201) +[HTML](103) +[PDF](536.93KB)
Response solutions for degenerate reversible harmonic oscillators
Wen Si
2021, 41(8) : 3951-3972 doi: 10.3934/dcds.2021023 +[Abstract](201) +[HTML](105) +[PDF](397.39KB)
Decay estimates for nonlinear Schrödinger equations
Chenjie Fan and Zehua Zhao
2021, 41(8) : 3973-3984 doi: 10.3934/dcds.2021024 +[Abstract](224) +[HTML](103) +[PDF](319.07KB)
Equilibria of an anisotropic nonlocal interaction equation: Analysis and numerics
José A. Carrillo, Bertram Düring, Lisa Maria Kreusser and Carola-Bibiane Schönlieb
2021, 41(8) : 3985-4012 doi: 10.3934/dcds.2021025 +[Abstract](241) +[HTML](102) +[PDF](1731.32KB)
Asymptotic behavior of entire solutions to reaction-diffusion equations in an infinite star graph
Shuichi Jimbo and Yoshihisa Morita
2021doi: 10.3934/dcds.2021026 +[Abstract](235) +[HTML](110) +[PDF](679.98KB)
On the dynamics of 3D electrified falling films
Jiao He and Rafael Granero-Belinchón
2021doi: 10.3934/dcds.2021027 +[Abstract](183) +[HTML](95) +[PDF](705.78KB)
Global generalized solutions to a chemotaxis model of capillary-sprout growth during tumor angiogenesis
Xueli Bai and Wenji Zhang
2021doi: 10.3934/dcds.2021028 +[Abstract](192) +[HTML](98) +[PDF](429.54KB)
Best approximation of orbits in iterated function systems
Saisai Shi, Bo Tan and Qinglong Zhou
2021doi: 10.3934/dcds.2021029 +[Abstract](231) +[HTML](98) +[PDF](381.07KB)
On multiplicity of semi-classical solutions to nonlinear Dirac equations of space-dimension $ n $
Yanheng Ding, Xiaojing Dong and Qi Guo
2021doi: 10.3934/dcds.2021030 +[Abstract](177) +[HTML](91) +[PDF](404.35KB)
Existence of solution for a class of heat equation in whole $ \mathbb{R}^N $
Claudianor O. Alves and Tahir Boudjeriou
2021doi: 10.3934/dcds.2021031 +[Abstract](152) +[HTML](88) +[PDF](419.68KB)
Coexistence and exclusion of competitive Kolmogorov systems with semi-Markovian switching
Dan Li and Hui Wan
2021doi: 10.3934/dcds.2021032 +[Abstract](199) +[HTML](103) +[PDF](504.1KB)
Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations
Mostafa Fazly and Yuan Li
2021doi: 10.3934/dcds.2021033 +[Abstract](168) +[HTML](88) +[PDF](443.91KB)
Local well-posedness for the derivative nonlinear Schrödinger equation with $ L^2 $-subcritical data
Shaoming Guo, Xianfeng Ren and Baoxiang Wang
2021doi: 10.3934/dcds.2021034 +[Abstract](199) +[HTML](118) +[PDF](572.43KB)
Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues
Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim and Doo Seok Lee
2021doi: 10.3934/dcds.2021035 +[Abstract](199) +[HTML](92) +[PDF](1894.09KB)
Singular double-phase systems with variable growth for the Baouendi-Grushin operator
Anouar Bahrouni and Vicenţiu D. Rădulescu
2021doi: 10.3934/dcds.2021036 +[Abstract](202) +[HTML](92) +[PDF](324.37KB)
Supercritical elliptic problems involving a Cordes like operator
Craig Cowan
2021doi: 10.3934/dcds.2021037 +[Abstract](134) +[HTML](52) +[PDF](446.39KB)
Permutations with restricted movement
Dor Elimelech
2021doi: 10.3934/dcds.2021038 +[Abstract](116) +[HTML](54) +[PDF](652.34KB)
PDEs on graphs for semi-supervised learning applied to first-person activity recognition in body-worn video
Hao Li, Honglin Chen, Matt Haberland, Andrea L. Bertozzi and P. Jeffrey Brantingham
2021doi: 10.3934/dcds.2021039 +[Abstract](114) +[HTML](77) +[PDF](2958.11KB)
Flows with the weak two-sided limit shadowing property
Jihoon Lee and Ngocthach Nguyen
2021doi: 10.3934/dcds.2021040 +[Abstract](147) +[HTML](51) +[PDF](364.93KB)
Partial regularity and the Minkowski dimension of singular points for suitable weak solutions to the 3D simplified Ericksen–Leslie system
Qiao Liu
2021doi: 10.3934/dcds.2021041 +[Abstract](116) +[HTML](53) +[PDF](507.04KB)
Dirichlet and transmission problems for anisotropic stokes and Navier-Stokes systems with L tensor coefficient under relaxed ellipticity condition
Mirela Kohr, Sergey E. Mikhailov and Wolfgang L. Wendland
2021doi: 10.3934/dcds.2021042 +[Abstract](133) +[HTML](72) +[PDF](628.31KB)
Pointwise gradient bounds for a class of very singular quasilinear elliptic equations
Minh-Phuong Tran and Thanh-Nhan Nguyen
2021doi: 10.3934/dcds.2021043 +[Abstract](246) +[HTML](65) +[PDF](395.04KB)
Centralizers of partially hyperbolic diffeomorphisms in dimension 3
Thomas Barthelmé and Andrey Gogolev
2021doi: 10.3934/dcds.2021044 +[Abstract](111) +[HTML](59) +[PDF](272.81KB)
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity
Suzete Maria Afonso, Vanessa Ramos and Jaqueline Siqueira
2021doi: 10.3934/dcds.2021045 +[Abstract](127) +[HTML](51) +[PDF](579.82KB)
Counting finite orbits for the flip systems of shifts of finite type
Azmeer Nordin and Mohd Salmi Md Noorani
2021doi: 10.3934/dcds.2021046 +[Abstract](121) +[HTML](48) +[PDF](333.28KB)
Floquet solutions for the Schrödinger equation with fast-oscillating quasi-periodic potentials
Yingte Sun
2021doi: 10.3934/dcds.2021047 +[Abstract](112) +[HTML](46) +[PDF](309.84KB)
On the critical decay for the wave equation with a cubic convolution in 3D
Tomoyuki Tanaka and Kyouhei Wakasa
2021doi: 10.3934/dcds.2021048 +[Abstract](129) +[HTML](46) +[PDF](384.97KB)
On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients
Hongjie Dong and Xinghong Pan
2021doi: 10.3934/dcds.2021049 +[Abstract](114) +[HTML](38) +[PDF](447.07KB)
Variational relations for metric mean dimension and rate distortion dimension
Tao Wang
2021doi: 10.3934/dcds.2021050 +[Abstract](130) +[HTML](47) +[PDF](360.16KB)
Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains
Hirokazu Saito and Xin Zhang
2021doi: 10.3934/dcds.2021051 +[Abstract](61) +[HTML](20) +[PDF](604.92KB)
A new approach to MGT-thermoviscoelasticity
Monica Conti, Vittorino Pata, Marta Pellicer and Ramon Quintanilla
2021doi: 10.3934/dcds.2021052 +[Abstract](62) +[HTML](21) +[PDF](429.33KB)
Differentiable invariant manifolds of nilpotent parabolic points
Clara Cufí-Cabré and Ernest Fontich
2021doi: 10.3934/dcds.2021053 +[Abstract](54) +[HTML](24) +[PDF](551.56KB)
Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials
Fangyi Qin, Jun Wang and Jing Yang
2021doi: 10.3934/dcds.2021054 +[Abstract](70) +[HTML](21) +[PDF](650.67KB)
A variational approach to three-phase traveling waves for a gradient system
Chiun-Chuan Chen, Hung-Yu Chien and Chih-Chiang Huang
2021doi: 10.3934/dcds.2021055 +[Abstract](114) +[HTML](69) +[PDF](928.46KB)
On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system
Lipeng Duan and Jun Yang
2021doi: 10.3934/dcds.2021056 +[Abstract](115) +[HTML](35) +[PDF](405.38KB)
On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points
Fei Liu, Xiaokai Liu and Fang Wang
2021doi: 10.3934/dcds.2021057 +[Abstract](90) +[HTML](33) +[PDF](637.1KB)
Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight
Alfonso Castro, Jorge Cossio, Sigifredo Herrón and Carlos Vélez
2021doi: 10.3934/dcds.2021058 +[Abstract](108) +[HTML](37) +[PDF](337.67KB)
An approximation of forward self-similar solutions to the 3D Navier-Stokes system
Francis Hounkpe and Gregory Seregin
2021doi: 10.3934/dcds.2021059 +[Abstract](106) +[HTML](41) +[PDF](377.84KB)
Refined construction of type II blow-up solutions for semilinear heat equations with Joseph–Lundgren supercritical nonlinearity
Asato Mukai and Yukihiro Seki
2021doi: 10.3934/dcds.2021060 +[Abstract](45) +[HTML](27) +[PDF](543.68KB)
Multiple positive bound state solutions for a critical Choquard equation
Claudianor O. Alves, Giovany M. Figueiredo and Riccardo Molle
2021doi: 10.3934/dcds.2021061 +[Abstract](63) +[HTML](23) +[PDF](453.96KB)
Singularity formation for compressible Euler equations with time-dependent damping
Ying Sui and Huimin Yu
2021doi: 10.3934/dcds.2021062 +[Abstract](49) +[HTML](23) +[PDF](419.9KB)
Symmetries of vector fields: The diffeomorphism centralizer
Davi Obata
2021doi: 10.3934/dcds.2021063 +[Abstract](41) +[HTML](25) +[PDF](369.1KB)
Asymptotic speed of spread for a nonlocal evolutionary-epidemic system
Lara Abi Rizk, Jean-Baptiste Burie and Arnaud Ducrot
2021doi: 10.3934/dcds.2021064 +[Abstract](56) +[HTML](23) +[PDF](393.7KB)
Convergence of nonlocal geometric flows to anisotropic mean curvature motion
Annalisa Cesaroni and Valerio Pagliari
2021doi: 10.3934/dcds.2021065 +[Abstract](60) +[HTML](35) +[PDF](383.21KB)
Modeling of crowds in regions with moving obstacles
Nadezhda Maltugueva and Nikolay Pogodaev
2021doi: 10.3934/dcds.2021066 +[Abstract](43) +[HTML](34) +[PDF](960.73KB)
A phase transition for circle maps with a flat spot and different critical exponents
Liviana Palmisano and Bertuel Tangue Ndawa
2021doi: 10.3934/dcds.2021067 +[Abstract](14) +[HTML](11) +[PDF](365.43KB)
Transfers of energy through fast diffusion channels in some resonant PDEs on the circle
Filippo Giuliani
2021doi: 10.3934/dcds.2021068 +[Abstract](31) +[HTML](16) +[PDF](437.94KB)
Einstein-Lichnerowicz type singular perturbations of critical nonlinear elliptic equations in dimension 3
Bruno Premoselli
2021doi: 10.3934/dcds.2021069 +[Abstract](18) +[HTML](7) +[PDF](350.7KB)
Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation
Agnid Banerjee and Ramesh Manna
2021doi: 10.3934/dcds.2021070 +[Abstract](14) +[HTML](10) +[PDF](410.15KB)
Global existence and decay rates of the solutions for a chemotaxis system with Lotka-Volterra type model for chemoattractant and repellent
Harumi Hattori and Aesha Lagha
2021doi: 10.3934/dcds.2021071 +[Abstract](14) +[HTML](8) +[PDF](398.64KB)
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](6882) +[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](4909) +[PDF](418.8KB) Cited By(284)
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](3647) +[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](6965) +[PDF](262.8KB) Cited By(200)
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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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
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Remarks on regularities for the 3D MHD equations
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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The problem Of blow-up in nonlinear parabolic equations
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Some questions looking for answers in dynamical systems
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The vorticity equation on a rotating sphere and the shallow fluid approximation
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Differentiability of the Hartman--Grobman linearization
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Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
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A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
Jie Shen and Xiaofeng Yang
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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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