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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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Modeling of crowds in regions with moving obstacles
Nadezhda Maltugueva and Nikolay Pogodaev
2021, 41(11) : 5009-5036 doi: 10.3934/dcds.2021066 +[Abstract](658) +[HTML](271) +[PDF](970.84KB)
A phase transition for circle maps with a flat spot and different critical exponents
Liviana Palmisano and Bertuel Tangue Ndawa
2021, 41(11) : 5037-5055 doi: 10.3934/dcds.2021067 +[Abstract](598) +[HTML](230) +[PDF](382.55KB)
Transfers of energy through fast diffusion channels in some resonant PDEs on the circle
Filippo Giuliani
2021, 41(11) : 5057-5085 doi: 10.3934/dcds.2021068 +[Abstract](732) +[HTML](232) +[PDF](454.96KB)
Einstein-Lichnerowicz type singular perturbations of critical nonlinear elliptic equations in dimension 3
Bruno Premoselli
2021, 41(11) : 5087-5103 doi: 10.3934/dcds.2021069 +[Abstract](550) +[HTML](205) +[PDF](368.31KB)
Carleman estimates for a class of variable coefficient degenerate elliptic operators with applications to unique continuation
Agnid Banerjee and Ramesh Manna
2021, 41(11) : 5105-5139 doi: 10.3934/dcds.2021070 +[Abstract](612) +[HTML](232) +[PDF](427.6KB)
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
2021, 41(11) : 5141-5164 doi: 10.3934/dcds.2021071 +[Abstract](462) +[HTML](237) +[PDF](415.72KB)
Uniqueness properties of the KAM curve
Frank Trujillo
2021, 41(11) : 5165-5182 doi: 10.3934/dcds.2021072 +[Abstract](380) +[HTML](189) +[PDF](348.38KB)
Nonlinear stability of elliptic equilibria in hamiltonian systems with exponential time estimates
Daniela Cárcamo-Díaz, Jesús F. Palacián, Claudio Vidal and Patricia Yanguas
2021, 41(11) : 5183-5208 doi: 10.3934/dcds.2021073 +[Abstract](489) +[HTML](198) +[PDF](480.01KB)
Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents
Minbo Yang, Fukun Zhao and Shunneng Zhao
2021, 41(11) : 5209-5241 doi: 10.3934/dcds.2021074 +[Abstract](537) +[HTML](193) +[PDF](507.99KB)
The graph of the logistic map is a tower
Roberto De Leo and James A. Yorke
2021, 41(11) : 5243-5269 doi: 10.3934/dcds.2021075 +[Abstract](522) +[HTML](223) +[PDF](4605.09KB)
Well-posedness and critical thresholds in a nonlocal Euler system with relaxation
Manas Bhatnagar and Hailiang Liu
2021, 41(11) : 5271-5289 doi: 10.3934/dcds.2021076 +[Abstract](511) +[HTML](181) +[PDF](383.19KB)
A proof by foliation that lawson's cones are $ A_{\Phi} $-minimizing
Connor Mooney and Yang Yang
2021, 41(11) : 5291-5302 doi: 10.3934/dcds.2021077 +[Abstract](366) +[HTML](180) +[PDF](1328.68KB)
Quadratic response and speed of convergence of invariant measures in the zero-noise limit
Stefano Galatolo and Hugo Marsan
2021, 41(11) : 5303-5327 doi: 10.3934/dcds.2021078 +[Abstract](337) +[HTML](161) +[PDF](441.86KB)
A multiplicity result for orthogonal geodesic chords in Finsler disks
Dario Corona
2021, 41(11) : 5329-5357 doi: 10.3934/dcds.2021079 +[Abstract](362) +[HTML](192) +[PDF](420.42KB)
On the decay in $ W^{1,\infty} $ for the 1D semilinear damped wave equation on a bounded domain
Debora Amadori and Fatima Al-Zahrà Aqel
2021, 41(11) : 5359-5396 doi: 10.3934/dcds.2021080 +[Abstract](400) +[HTML](172) +[PDF](535.89KB)
A class of prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in $ \mathbb{H}^{n+1} $
Qiang Tu
2021, 41(11) : 5397-5407 doi: 10.3934/dcds.2021081 +[Abstract](333) +[HTML](175) +[PDF](379.96KB)
Local well-posedness for the inhomogeneous nonlinear Schrödinger equation
Lassaad Aloui and Slim Tayachi
2021, 41(11) : 5409-5437 doi: 10.3934/dcds.2021082 +[Abstract](525) +[HTML](197) +[PDF](501.54KB)
Fractional perimeters on the sphere
Andreas Kreuml and Olaf Mordhorst
2021, 41(11) : 5439-5454 doi: 10.3934/dcds.2021083 +[Abstract](367) +[HTML](176) +[PDF](378.11KB)
On trigonometric skew-products over irrational circle-rotations
Hans Koch
2021, 41(11) : 5455-5471 doi: 10.3934/dcds.2021084 +[Abstract](317) +[HTML](178) +[PDF](1183.99KB)
Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured euclidean space
Kin Ming Hui and Jinwan Park
2021, 41(11) : 5473-5508 doi: 10.3934/dcds.2021085 +[Abstract](426) +[HTML](188) +[PDF](497.76KB)
Dynamics of particles on a curve with pairwise hyper-singular repulsion
Douglas Hardin, Edward B. Saff, Ruiwen Shu and Eitan Tadmor
2021doi: 10.3934/dcds.2021086 +[Abstract](353) +[HTML](175) +[PDF](695.6KB)
Hearing the shape of right triangle billiard tables
Yang Shen and Jiazhong Yang
2021doi: 10.3934/dcds.2021087 +[Abstract](290) +[HTML](187) +[PDF](3209.84KB)
Concentration phenomena for magnetic Kirchhoff equations with critical growth
Chao Ji and Vicenţiu D. Rădulescu
2021doi: 10.3934/dcds.2021088 +[Abstract](358) +[HTML](170) +[PDF](502.15KB)
Classification of transitive group actions
Kesong Yan, Qian Liu and Fanping Zeng
2021doi: 10.3934/dcds.2021089 +[Abstract](265) +[HTML](142) +[PDF](471.66KB)
Well-posedness of the two-phase flow problem in incompressible MHD
Changyan Li and Hui Li
2021doi: 10.3934/dcds.2021090 +[Abstract](305) +[HTML](127) +[PDF](504.75KB)
Period tripling and quintupling renormalizations below $ C^2 $ space
Rohit Kumar and V.V.M.S. Chandramouli
2021doi: 10.3934/dcds.2021091 +[Abstract](308) +[HTML](136) +[PDF](844.25KB)
The nonlinear fractional relativistic Schrödinger equation: Existence, multiplicity, decay and concentration results
Vincenzo Ambrosio
2021doi: 10.3934/dcds.2021092 +[Abstract](322) +[HTML](126) +[PDF](628.39KB)
Dispersive estimates for the wave and the Klein-Gordon equations in large time inside the Friedlander domain
Oana Ivanovici
2021doi: 10.3934/dcds.2021093 +[Abstract](264) +[HTML](119) +[PDF](575.76KB)
Extinction or coexistence in periodic Kolmogorov systems of competitive type
Isabel Coelho, Carlota Rebelo and Elisa Sovrano
2021doi: 10.3934/dcds.2021094 +[Abstract](279) +[HTML](130) +[PDF](377.55KB)
Grassmannian reduction of cucker-smale systems and dynamical opinion games
Daniel Lear, David N. Reynolds and Roman Shvydkoy
2021doi: 10.3934/dcds.2021095 +[Abstract](225) +[HTML](119) +[PDF](563.04KB)
Stabilization of nonautonomous parabolic equations by a single moving actuator
Behzad Azmi, Karl Kunisch and Sérgio S. Rodrigues
2021doi: 10.3934/dcds.2021096 +[Abstract](247) +[HTML](114) +[PDF](1557.31KB)
Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces
Wei Yan, Yimin Zhang, Yongsheng Li and Jinqiao Duan
2021doi: 10.3934/dcds.2021097 +[Abstract](204) +[HTML](114) +[PDF](598.89KB)
Sharp critical thresholds in a hyperbolic system with relaxation
Manas Bhatnagar and Hailiang Liu
2021doi: 10.3934/dcds.2021098 +[Abstract](183) +[HTML](118) +[PDF](467.97KB)
Discrete spectrum for amenable group actions
Tao Yu, Guohua Zhang and Ruifeng Zhang
2021doi: 10.3934/dcds.2021099 +[Abstract](208) +[HTML](110) +[PDF](490.37KB)
On the number of invariant measures for random expanding maps in higher dimensions
Fawwaz Batayneh and Cecilia González-Tokman
2021doi: 10.3934/dcds.2021100 +[Abstract](249) +[HTML](121) +[PDF](570.84KB)
Maximal chain continuous factor
Noriaki Kawaguchi
2021doi: 10.3934/dcds.2021101 +[Abstract](213) +[HTML](110) +[PDF](376.1KB)
Bifurcations in asymptotically autonomous Hamiltonian systems under oscillatory perturbations
Oskar A. Sultanov
2021doi: 10.3934/dcds.2021102 +[Abstract](226) +[HTML](125) +[PDF](1679.17KB)
On pushed wavefronts of monostable equation with unimodal delayed reaction
Karel Hasík, Jana Kopfová, Petra Nábělková and Sergei Trofimchuk
2021doi: 10.3934/dcds.2021103 +[Abstract](218) +[HTML](139) +[PDF](3955.42KB)
Global wellposedness of nutrient-taxis systems derived by a food metric
Jaewook Ahn, Sun-Ho Choi and Minha Yoo
2021doi: 10.3934/dcds.2021104 +[Abstract](254) +[HTML](120) +[PDF](348.99KB)
Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity
Diego Berti, Andrea Corli and Luisa Malaguti
2021doi: 10.3934/dcds.2021105 +[Abstract](258) +[HTML](116) +[PDF](387.56KB)
On the compactness threshold in the critical Kirchhoff equation
Erisa Hasani and Kanishka Perera
2021doi: 10.3934/dcds.2021106 +[Abstract](494) +[HTML](122) +[PDF](501.7KB)
On the number of positive solutions to an indefinite parameter-dependent Neumann problem
Guglielmo Feltrin, Elisa Sovrano and Andrea Tellini
2021doi: 10.3934/dcds.2021107 +[Abstract](241) +[HTML](101) +[PDF](871.3KB)
Upper semicontinuity of pullback attractors for non-autonomous lattice systems under singular perturbations
Na Lei and Shengfan Zhou
2021doi: 10.3934/dcds.2021108 +[Abstract](196) +[HTML](78) +[PDF](609.76KB)
A semilinear problem with a gradient term in the nonlinearity
Ignacio Guerra
2021doi: 10.3934/dcds.2021110 +[Abstract](172) +[HTML](75) +[PDF](334.75KB)
Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems
Tuhina Mukherjee, Patrizia Pucci and Mingqi Xiang
2021doi: 10.3934/dcds.2021111 +[Abstract](198) +[HTML](90) +[PDF](526.22KB)
Orbit counting in polarized dynamical systems
Wade Hindes
2021doi: 10.3934/dcds.2021112 +[Abstract](115) +[HTML](66) +[PDF](584.26KB)
The relaxation limit of bipolar fluid models
Nuno J. Alves and Athanasios E. Tzavaras
2021doi: 10.3934/dcds.2021113 +[Abstract](127) +[HTML](56) +[PDF](447.84KB)
Families of vector fields with many numerical invariants
Nataliya Goncharuk and Yury Kudryashov
2021doi: 10.3934/dcds.2021114 +[Abstract](110) +[HTML](70) +[PDF](510.08KB)
On a curvature flow in a band domain with unbounded boundary slopes
Lixia Yuan and Wei Zhao
2021doi: 10.3934/dcds.2021115 +[Abstract](110) +[HTML](60) +[PDF](618.91KB)
Shadowing for families of endomorphisms of generalized group shifts
Xuan Kien Phung
2021doi: 10.3934/dcds.2021116 +[Abstract](127) +[HTML](55) +[PDF](418.49KB)
Estimates the upper bounds of Dirichlet eigenvalues for fractional Laplacian
Hua Chen and Hong-Ge Chen
2021doi: 10.3934/dcds.2021117 +[Abstract](127) +[HTML](68) +[PDF](500.23KB)
Subhyperbolic rational maps on boundaries of hyperbolic components
Yan Gao, Luxian Yang and Jinsong Zeng
2021doi: 10.3934/dcds.2021118 +[Abstract](98) +[HTML](46) +[PDF](331.42KB)
The geodesic flow on nilpotent Lie groups of steps two and three
Gabriela P. Ovando
2021doi: 10.3934/dcds.2021119 +[Abstract](100) +[HTML](42) +[PDF](530.75KB)
Inducing schemes for multi-dimensional piecewise expanding maps
Peyman Eslami
2021doi: 10.3934/dcds.2021120 +[Abstract](109) +[HTML](51) +[PDF](483.38KB)
Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces II
Kazuhiro Ishige and Yujiro Tateishi
2021doi: 10.3934/dcds.2021121 +[Abstract](117) +[HTML](37) +[PDF](651.86KB)
The critical points of the elastic energy among curves pinned at endpoints
Kensuke Yoshizawa
2021doi: 10.3934/dcds.2021122 +[Abstract](101) +[HTML](43) +[PDF](1431.6KB)
The Brinkman-Fourier system with ideal gas equilibrium
Chun Liu and Jan-Eric Sulzbach
2021doi: 10.3934/dcds.2021123 +[Abstract](112) +[HTML](43) +[PDF](515.34KB)
Exact null-controllability of interconnected abstract evolution equations with unbounded input operators
Benzion Shklyar
2021doi: 10.3934/dcds.2021124 +[Abstract](85) +[HTML](41) +[PDF](302.35KB)
A log–exp elliptic equation in the plane
Giovany Figueiredo, Marcelo Montenegro and Matheus F. Stapenhorst
2021doi: 10.3934/dcds.2021125 +[Abstract](150) +[HTML](42) +[PDF](407.79KB)
Exact description of SIR-Bass epidemics on 1D lattices
Gadi Fibich and Samuel Nordmann
2021doi: 10.3934/dcds.2021126 +[Abstract](103) +[HTML](43) +[PDF](460.53KB)
$ W^{1, p} $ estimates for elliptic problems with drift terms in Lipschitz domains
Bojing Shi
2021doi: 10.3934/dcds.2021127 +[Abstract](116) +[HTML](48) +[PDF](362.92KB)
Aubry-Mather theory for contact Hamiltonian systems II
Kaizhi Wang, Lin Wang and Jun Yan
2021doi: 10.3934/dcds.2021128 +[Abstract](68) +[HTML](45) +[PDF](588.98KB)
Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity
Bassam Fayad and Maria Saprykina
2021doi: 10.3934/dcds.2021129 +[Abstract](66) +[HTML](28) +[PDF](178.97KB)
Propagating fronts for a viscous Hamer-type system
Giada Cianfarani Carnevale, Corrado Lattanzio and Corrado Mascia
2021doi: 10.3934/dcds.2021130 +[Abstract](63) +[HTML](27) +[PDF](427.65KB)
Forward triplets and topological entropy on trees
Lluís Alsedà, David Juher and Francesc Mañosas
2021doi: 10.3934/dcds.2021131 +[Abstract](67) +[HTML](39) +[PDF](481.04KB)
Pullback attractors for 2D MHD equations on time-varying domains
Daomin Cao, Xiaoya Song and Chunyou Sun
2021doi: 10.3934/dcds.2021132 +[Abstract](51) +[HTML](21) +[PDF](571.28KB)
On the fractional susceptibility function of piecewise expanding maps
Magnus Aspenberg, Viviane Baladi, Juho Leppänen and Tomas Persson
2021doi: 10.3934/dcds.2021133 +[Abstract](49) +[HTML](21) +[PDF](284.65KB)
Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics
Hansol Park
2021doi: 10.3934/dcds.2021134 +[Abstract](48) +[HTML](23) +[PDF](561.5KB)
Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction
Giovanni Colombo, Paolo Gidoni and Emilio Vilches
2021doi: 10.3934/dcds.2021135 +[Abstract](58) +[HTML](24) +[PDF](536.48KB)
Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis
Guoqiang Ren and Bin Liu
2021doi: 10.3934/dcds.2021136 +[Abstract](61) +[HTML](38) +[PDF](511.96KB)
Singular weighted sharp Trudinger-Moser inequalities defined on $ \mathbb{R}^N $ and applications to elliptic nonlinear equations
Sami Aouaoui and Rahma Jlel
2021doi: 10.3934/dcds.2021137 +[Abstract](59) +[HTML](24) +[PDF](613.85KB)
Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle
Stefano Galatolo and Alfonso Sorrentino
2021doi: 10.3934/dcds.2021138 +[Abstract](51) +[HTML](14) +[PDF](589.44KB)
Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts
Kengo Matsumoto
2021doi: 10.3934/dcds.2021139 +[Abstract](44) +[HTML](15) +[PDF](352.01KB)
Pure strictly uniform models of non-ergodic measure automorphisms
Tomasz Downarowicz and Benjamin Weiss
2021doi: 10.3934/dcds.2021140 +[Abstract](45) +[HTML](12) +[PDF](1588.76KB)
Global stability solution of the 2D MHD equations with mixed partial dissipation
Yana Guo, Yan Jia and Bo-Qing Dong
2021doi: 10.3934/dcds.2021141 +[Abstract](62) +[HTML](15) +[PDF](307.3KB)
The nonlocal-interaction equation near attracting manifolds
Francesco S. Patacchini and Dejan Slepčev
2021doi: 10.3934/dcds.2021142 +[Abstract](47) +[HTML](14) +[PDF](565.89KB)
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](8321) +[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](5574) +[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](4182) +[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](7771) +[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](5622) +[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](6980) +[PDF](246.2KB) Cited By(198)
Partial regularity of the dynamic system modeling the flow of liquid crystals
Fanghua Lin and Chun Liu
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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](6211) +[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
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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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2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](5582) +[HTML](366) +[PDF](531.03KB) PDF Downloads(1728)
The vorticity equation on a rotating sphere and the shallow fluid approximation
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2019, 39(11) : 6261-6276 doi: 10.3934/dcds.2019273 +[Abstract](1764) +[HTML](163) +[PDF](370.02KB) PDF Downloads(1225)
Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
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2012, 32(7) : 2565-2582 doi: 10.3934/dcds.2012.32.2565 +[Abstract](3596) +[PDF](444.9KB) PDF Downloads(1035)
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](8321) +[PDF](382.7KB) PDF Downloads(751)
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](7911) +[PDF](401.1KB) PDF Downloads(730)
On the spectral theory of positive operators and PDE applications
Kung-Ching Chang, Xuefeng Wang and Xie Wu
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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](6081) +[HTML](893) +[PDF](472.85KB) PDF Downloads(588)
On Geometric Mechanics
Jean-Marie Souriau
2007, 19(3) : 595-607 doi: 10.3934/dcds.2007.19.595 +[Abstract](2397) +[PDF](183.4KB) PDF Downloads(581)

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