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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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Asymptotic behavior of entire solutions to reaction-diffusion equations in an infinite star graph
Shuichi Jimbo and Yoshihisa Morita
2021, 41(9) : 4013-4039 doi: 10.3934/dcds.2021026 +[Abstract](574) +[HTML](236) +[PDF](696.14KB)
On the dynamics of 3D electrified falling films
Jiao He and Rafael Granero-Belinchón
2021, 41(9) : 4041-4064 doi: 10.3934/dcds.2021027 +[Abstract](363) +[HTML](181) +[PDF](722.63KB)
Global generalized solutions to a chemotaxis model of capillary-sprout growth during tumor angiogenesis
Xueli Bai and Wenji Zhang
2021, 41(9) : 4065-4083 doi: 10.3934/dcds.2021028 +[Abstract](384) +[HTML](180) +[PDF](447.07KB)
Best approximation of orbits in iterated function systems
Saisai Shi, Bo Tan and Qinglong Zhou
2021, 41(9) : 4085-4104 doi: 10.3934/dcds.2021029 +[Abstract](449) +[HTML](191) +[PDF](398.14KB)
On multiplicity of semi-classical solutions to nonlinear Dirac equations of space-dimension $ n $
Yanheng Ding, Xiaojing Dong and Qi Guo
2021, 41(9) : 4105-4123 doi: 10.3934/dcds.2021030 +[Abstract](355) +[HTML](176) +[PDF](422.37KB)
Existence of solution for a class of heat equation in whole $ \mathbb{R}^N $
Claudianor O. Alves and Tahir Boudjeriou
2021, 41(9) : 4125-4144 doi: 10.3934/dcds.2021031 +[Abstract](353) +[HTML](167) +[PDF](436.45KB)
Coexistence and exclusion of competitive Kolmogorov systems with semi-Markovian switching
Dan Li and Hui Wan
2021, 41(9) : 4145-4183 doi: 10.3934/dcds.2021032 +[Abstract](447) +[HTML](184) +[PDF](514.95KB)
Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations
Mostafa Fazly and Yuan Li
2021, 41(9) : 4185-4206 doi: 10.3934/dcds.2021033 +[Abstract](362) +[HTML](164) +[PDF](460.98KB)
Local well-posedness for the derivative nonlinear Schrödinger equation with $ L^2 $-subcritical data
Shaoming Guo, Xianfeng Ren and Baoxiang Wang
2021, 41(9) : 4207-4253 doi: 10.3934/dcds.2021034 +[Abstract](397) +[HTML](212) +[PDF](589.25KB)
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
2021, 41(9) : 4255-4281 doi: 10.3934/dcds.2021035 +[Abstract](391) +[HTML](180) +[PDF](1952.82KB)
Singular double-phase systems with variable growth for the Baouendi-Grushin operator
Anouar Bahrouni and Vicenţiu D. Rădulescu
2021, 41(9) : 4283-4296 doi: 10.3934/dcds.2021036 +[Abstract](802) +[HTML](180) +[PDF](349.33KB)
Supercritical elliptic problems involving a Cordes like operator
Craig Cowan
2021, 41(9) : 4297-4318 doi: 10.3934/dcds.2021037 +[Abstract](319) +[HTML](131) +[PDF](464.46KB)
Permutations with restricted movement
Dor Elimelech
2021, 41(9) : 4319-4349 doi: 10.3934/dcds.2021038 +[Abstract](314) +[HTML](134) +[PDF](676.34KB)
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
2021, 41(9) : 4351-4373 doi: 10.3934/dcds.2021039 +[Abstract](367) +[HTML](185) +[PDF](2975.15KB)
Flows with the weak two-sided limit shadowing property
Jihoon Lee and Ngocthach Nguyen
2021, 41(9) : 4375-4395 doi: 10.3934/dcds.2021040 +[Abstract](370) +[HTML](146) +[PDF](389.52KB)
Partial regularity and the Minkowski dimension of singular points for suitable weak solutions to the 3D simplified Ericksen–Leslie system
Qiao Liu
2021, 41(9) : 4397-4419 doi: 10.3934/dcds.2021041 +[Abstract](282) +[HTML](148) +[PDF](523.14KB)
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
2021, 41(9) : 4421-4460 doi: 10.3934/dcds.2021042 +[Abstract](384) +[HTML](175) +[PDF](631.89KB)
Pointwise gradient bounds for a class of very singular quasilinear elliptic equations
Minh-Phuong Tran and Thanh-Nhan Nguyen
2021, 41(9) : 4461-4476 doi: 10.3934/dcds.2021043 +[Abstract](472) +[HTML](145) +[PDF](412.32KB)
Centralizers of partially hyperbolic diffeomorphisms in dimension 3
Thomas Barthelmé and Andrey Gogolev
2021, 41(9) : 4477-4484 doi: 10.3934/dcds.2021044 +[Abstract](279) +[HTML](154) +[PDF](289.54KB)
Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity
Suzete Maria Afonso, Vanessa Ramos and Jaqueline Siqueira
2021, 41(9) : 4485-4513 doi: 10.3934/dcds.2021045 +[Abstract](382) +[HTML](139) +[PDF](624.19KB)
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](300) +[HTML](125) +[PDF](333.28KB)
Floquet solutions for the Schrödinger equation with fast-oscillating quasi-periodic potentials
Yingte Sun
2021doi: 10.3934/dcds.2021047 +[Abstract](246) +[HTML](120) +[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](357) +[HTML](125) +[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](244) +[HTML](119) +[PDF](447.07KB)
Variational relations for metric mean dimension and rate distortion dimension
Tao Wang
2021doi: 10.3934/dcds.2021050 +[Abstract](379) +[HTML](122) +[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](236) +[HTML](92) +[PDF](605.01KB)
A new approach to MGT-thermoviscoelasticity
Monica Conti, Vittorino Pata, Marta Pellicer and Ramon Quintanilla
2021doi: 10.3934/dcds.2021052 +[Abstract](203) +[HTML](92) +[PDF](429.33KB)
Differentiable invariant manifolds of nilpotent parabolic points
Clara Cufí-Cabré and Ernest Fontich
2021doi: 10.3934/dcds.2021053 +[Abstract](179) +[HTML](95) +[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](251) +[HTML](103) +[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](256) +[HTML](149) +[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](297) +[HTML](125) +[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](210) +[HTML](111) +[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](324) +[HTML](118) +[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](251) +[HTML](126) +[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](210) +[HTML](112) +[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](240) +[HTML](100) +[PDF](453.96KB)
Singularity formation for compressible Euler equations with time-dependent damping
Ying Sui and Huimin Yu
2021doi: 10.3934/dcds.2021062 +[Abstract](170) +[HTML](97) +[PDF](419.9KB)
Symmetries of vector fields: The diffeomorphism centralizer
Davi Obata
2021doi: 10.3934/dcds.2021063 +[Abstract](198) +[HTML](105) +[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](257) +[HTML](104) +[PDF](393.7KB)
Convergence of nonlocal geometric flows to anisotropic mean curvature motion
Annalisa Cesaroni and Valerio Pagliari
2021doi: 10.3934/dcds.2021065 +[Abstract](215) +[HTML](112) +[PDF](383.21KB)
Modeling of crowds in regions with moving obstacles
Nadezhda Maltugueva and Nikolay Pogodaev
2021doi: 10.3934/dcds.2021066 +[Abstract](162) +[HTML](117) +[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](207) +[HTML](85) +[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](343) +[HTML](99) +[PDF](437.94KB)
Einstein-Lichnerowicz type singular perturbations of critical nonlinear elliptic equations in dimension 3
Bruno Premoselli
2021doi: 10.3934/dcds.2021069 +[Abstract](179) +[HTML](89) +[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](221) +[HTML](103) +[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](195) +[HTML](102) +[PDF](398.64KB)
Uniqueness properties of the KAM curve
Frank Trujillo
2021doi: 10.3934/dcds.2021072 +[Abstract](133) +[HTML](70) +[PDF](371.83KB)
Nonlinear stability of elliptic equilibria in hamiltonian systems with exponential time estimates
Daniela Cárcamo-Díaz, Jesús F. Palacián, Claudio Vidal and Patricia Yanguas
2021doi: 10.3934/dcds.2021073 +[Abstract](169) +[HTML](63) +[PDF](570.87KB)
Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents
Minbo Yang, Fukun Zhao and Shunneng Zhao
2021doi: 10.3934/dcds.2021074 +[Abstract](189) +[HTML](71) +[PDF](601.94KB)
The graph of the logistic map is a tower
Roberto De Leo and James A. Yorke
2021doi: 10.3934/dcds.2021075 +[Abstract](181) +[HTML](84) +[PDF](4674.96KB)
Well-posedness and critical thresholds in a nonlocal Euler system with relaxation
Manas Bhatnagar and Hailiang Liu
2021doi: 10.3934/dcds.2021076 +[Abstract](168) +[HTML](62) +[PDF](435.17KB)
A proof by foliation that lawson's cones are $ A_{\Phi} $-minimizing
Connor Mooney and Yang Yang
2021doi: 10.3934/dcds.2021077 +[Abstract](129) +[HTML](58) +[PDF](504.71KB)
Quadratic response and speed of convergence of invariant measures in the zero-noise limit
Stefano Galatolo and Hugo Marsan
2021doi: 10.3934/dcds.2021078 +[Abstract](116) +[HTML](50) +[PDF](424.66KB)
A multiplicity result for orthogonal geodesic chords in Finsler disks
Dario Corona
2021doi: 10.3934/dcds.2021079 +[Abstract](113) +[HTML](55) +[PDF](396.01KB)
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
2021doi: 10.3934/dcds.2021080 +[Abstract](136) +[HTML](57) +[PDF](526.34KB)
A class of prescribed shifted Gauss curvature equations for horo-convex hypersurfaces in $ \mathbb{H}^{n+1} $
Qiang Tu
2021doi: 10.3934/dcds.2021081 +[Abstract](104) +[HTML](56) +[PDF](362.51KB)
Local well-posedness for the inhomogeneous nonlinear Schrödinger equation
Lassaad Aloui and Slim Tayachi
2021doi: 10.3934/dcds.2021082 +[Abstract](156) +[HTML](61) +[PDF](484.37KB)
Fractional perimeters on the sphere
Andreas Kreuml and Olaf Mordhorst
2021doi: 10.3934/dcds.2021083 +[Abstract](113) +[HTML](55) +[PDF](353.99KB)
On trigonometric skew-products over irrational circle-rotations
Hans Koch
2021doi: 10.3934/dcds.2021084 +[Abstract](69) +[HTML](21) +[PDF](1166.8KB)
Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured euclidean space
Kin Ming Hui and Jinwan Park
2021doi: 10.3934/dcds.2021085 +[Abstract](140) +[HTML](65) +[PDF](480.54KB)
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](122) +[HTML](43) +[PDF](695.6KB)
Hearing the shape of right triangle billiard tables
Yang Shen and Jiazhong Yang
2021doi: 10.3934/dcds.2021087 +[Abstract](103) +[HTML](61) +[PDF](3209.84KB)
Concentration phenomena for magnetic Kirchhoff equations with critical growth
Chao Ji and Vicenţiu D. Rădulescu
2021doi: 10.3934/dcds.2021088 +[Abstract](132) +[HTML](61) +[PDF](502.15KB)
Classification of transitive group actions
Kesong Yan, Qian Liu and Fanping Zeng
2021doi: 10.3934/dcds.2021089 +[Abstract](2) +[HTML](3) +[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](2) +[HTML](1) +[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](2) +[HTML](1) +[PDF](844.25KB)
The nonlinear fractional relativistic Schrödinger equation: Existence, multiplicity, decay and concentration results
Vincenzo Ambrosio
2021doi: 10.3934/dcds.2021092 +[Abstract](2) +[HTML](1) +[PDF](622.66KB)
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](2) +[HTML](1) +[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](2) +[HTML](1) +[PDF](377.55KB)
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](7462) +[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](5177) +[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](3882) +[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](7274) +[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
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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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Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
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Differentiability of the Hartman--Grobman linearization
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Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
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On the spectral theory of positive operators and PDE applications
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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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