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Discrete and 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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Well-posedness and critical index set of the Cauchy problem for the coupled KdV-KdV systems on $ \mathbb{T} $
Xin Yang and Bing-Yu Zhang
2022, 42(11) : 5167-5199 doi: 10.3934/dcds.2022090 +[Abstract](276) +[HTML](106) +[PDF](534.48KB)
Global weak solutions to a chemotaxis-Navier-Stokes system in $ \mathbb{R}^3 $
Kyungkeun Kang, Jihoon Lee and Michael Winkler
2022, 42(11) : 5201-5222 doi: 10.3934/dcds.2022091 +[Abstract](232) +[HTML](71) +[PDF](396.12KB)
The dimensional estimates of exponential growth solutions to uniformly elliptic equations of non-divergence form
Lidan Wang, Lihe Wang and Chunqin Zhou
2022, 42(11) : 5223-5238 doi: 10.3934/dcds.2022092 +[Abstract](260) +[HTML](48) +[PDF](339.28KB)
Long exact sequences of homology groups of étale groupoids
Hiroki Matui
2022, 42(11) : 5239-5271 doi: 10.3934/dcds.2022095 +[Abstract](166) +[HTML](55) +[PDF](509.75KB)
Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold
Saikat Mazumdar and Jérôme Vétois
2022, 42(11) : 5273-5287 doi: 10.3934/dcds.2022097 +[Abstract](147) +[HTML](56) +[PDF](327.59KB)
Fiber entropy and algorithmic complexity of random orbits
Elias Zimmermann
2022, 42(11) : 5289-5308 doi: 10.3934/dcds.2022098 +[Abstract](163) +[HTML](45) +[PDF](368.15KB)
Mingled hyperbolicities: Ergodic properties and bifurcation phenomena (an approach using concavity)
Lorenzo J. Díaz, Katrin Gelfert and Michał Rams
2022, 42(11) : 5309-5376 doi: 10.3934/dcds.2022100 +[Abstract](147) +[HTML](56) +[PDF](1172.72KB)
Monotonicity of entropy for unimodal real quadratic rational maps
Yan Gao
2022, 42(11) : 5377-5386 doi: 10.3934/dcds.2022101 +[Abstract](150) +[HTML](90) +[PDF](392.15KB)
An $ L^{q}\rightarrow L^{r} $ estimate for rough Fourier integral operators and its applications
Jinhui Li and Guangqing Wang
2022, 42(11) : 5387-5397 doi: 10.3934/dcds.2022102 +[Abstract](151) +[HTML](46) +[PDF](354.78KB)
Spectral theory of spin substitutions
Natalie Priebe Frank and Neil Mañibo
2022, 42(11) : 5399-5435 doi: 10.3934/dcds.2022105 +[Abstract](204) +[HTML](56) +[PDF](1306.22KB)
The general maximum principle for stochastic control problems with singular controls
Yuanzhuo Song and Zhen Wu
2022, 42(11) : 5437-5451 doi: 10.3934/dcds.2022106 +[Abstract](147) +[HTML](40) +[PDF](353.19KB)
Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems
Daniel Adams, Manh Hong Duong and Gonçalo dos Reis
2022, 42(11) : 5453-5486 doi: 10.3934/dcds.2022109 +[Abstract](176) +[HTML](81) +[PDF](459.03KB)
Energy conservation and regularity for the 3D magneto-hydrodynamics equations
Wenke Tan and Fan Wu
2022, 42(11) : 5487-5508 doi: 10.3934/dcds.2022110 +[Abstract](161) +[HTML](59) +[PDF](443.1KB)
An uncountable ergodic Roth theorem and applications
Polona Durcik, Rachel Greenfeld, Annina Iseli, Asgar Jamneshan and José Madrid
2022, 42(11) : 5509-5540 doi: 10.3934/dcds.2022111 +[Abstract](193) +[HTML](54) +[PDF](512.3KB)
Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical systems
Claudio Bonanno and Tanja I. Schindler
2022, 42(11) : 5541-5576 doi: 10.3934/dcds.2022113 +[Abstract](182) +[HTML](50) +[PDF](475.73KB)
Strong time-periodic solutions to chemotaxis–Navier–Stokes equations on bounded domains
Keiichi Watanabe
2022, 42(11) : 5577-5590 doi: 10.3934/dcds.2022114 +[Abstract](169) +[HTML](48) +[PDF](348.0KB)
Minimal P-cyclic periodic brake orbits in Hamiltonian systems
Xiaorui Li and Duanzhi Zhang
2022, 42(11) : 5591-5611 doi: 10.3934/dcds.2022115 +[Abstract](173) +[HTML](51) +[PDF](398.96KB)
A game theoretical approximation for a parabolic/elliptic system with different operators
Alfredo Miranda and Julio D. Rossi
2022doi: 10.3934/dcds.2022034 +[Abstract](332) +[HTML](141) +[PDF](449.12KB)
Examples of finite time blow up in mass dissipative reaction-diffusion systems with superquadratic growth
Michel Pierre and Didier Schmitt
2022doi: 10.3934/dcds.2022039 +[Abstract](306) +[HTML](228) +[PDF](401.97KB)
Radon measure-valued solutions of unsteady filtration equations
Maria Michaela Porzio, Flavia Smarrazzo and Alberto Tesei
2022doi: 10.3934/dcds.2022040 +[Abstract](257) +[HTML](109) +[PDF](459.36KB)
Stability of a class of action functionals depending on convex functions
Luigi Ambrosio and Camillo Brena
2022doi: 10.3934/dcds.2022055 +[Abstract](246) +[HTML](99) +[PDF](317.18KB)
Elliptic systems with nonlinear diffusion and a convection term
Lucio Boccardo and Luigi Orsina
2022doi: 10.3934/dcds.2022056 +[Abstract](351) +[HTML](116) +[PDF](353.88KB)
Controlled boundary explosions: Dynamics after blow-up for some semilinear problems with global controls
Alfonso Carlos Casal, Gregorio Díaz, Jesús Ildefonso Díaz and José Manuel Vegas
2022doi: 10.3934/dcds.2022075 +[Abstract](188) +[HTML](81) +[PDF](602.15KB)
Symmetrization for fractional nonlinear elliptic problems
Vincenzo Ferone and Bruno Volzone
2022doi: 10.3934/dcds.2022076 +[Abstract](209) +[HTML](81) +[PDF](479.12KB)
Large time behavior for a nonlocal nonlinear gradient flow
Feng Li and Erik Lindgren
2022doi: 10.3934/dcds.2022079 +[Abstract](306) +[HTML](62) +[PDF](461.19KB)
Parabolic methods for ultraspherical interpolation inequalities
Jean Dolbeault and An Zhang
2022doi: 10.3934/dcds.2022080 +[Abstract](175) +[HTML](73) +[PDF](452.78KB)
Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations
Matteo Bonforte, Jean Dolbeault, Bruno Nazaret and Nikita Simonov
2022doi: 10.3934/dcds.2022093 +[Abstract](222) +[HTML](58) +[PDF](854.07KB)
A new convergence proof for approximations of the Stefan problem
Robert Eymard and Thierry Gallouët
2022doi: 10.3934/dcds.2022094 +[Abstract](129) +[HTML](54) +[PDF](331.74KB)
Bulk-boundary eigenvalues for Bilaplacian problems
Davide Buoso, Carles Falcó, María del Mar González and Manuel Miranda
2022doi: 10.3934/dcds.2022096 +[Abstract](213) +[HTML](79) +[PDF](739.5KB)
Universal estimates and Liouville theorems for superlinear problems without scale invariance
Philippe Souplet
2022doi: 10.3934/dcds.2022099 +[Abstract](99) +[HTML](45) +[PDF](491.51KB)
The stickiness property for antisymmetric nonlocal minimal graphs
Benjamin Baronowitz, Serena Dipierro and Enrico Valdinoci
2022doi: 10.3934/dcds.2022103 +[Abstract](104) +[HTML](101) +[PDF](522.46KB)
The porous medium equation with large data on Cartan-Hadamard manifolds under general curvature bounds
Gabriele Grillo, Matteo Muratori and Fabio Punzo
2022doi: 10.3934/dcds.2022104 +[Abstract](87) +[HTML](44) +[PDF](434.23KB)
Trace and boundary singularities of positive solutions of a class of quasilinear equations
Marie-Françoise Bidaut-Véron and Laurent Véron
2022doi: 10.3934/dcds.2022107 +[Abstract](136) +[HTML](97) +[PDF](442.83KB)
Uniform tail estimates and $ L^p( {\mathbb{R}}^N) $-convergence for finite-difference approximations of nonlinear diffusion equations
Félix del Teso, Jørgen Endal and Espen R. Jakobsen
2022doi: 10.3934/dcds.2022108 +[Abstract](113) +[HTML](47) +[PDF](440.72KB)
The Cauchy-Dirichlet problem for singular nonlocal diffusions on bounded domains
Matteo Bonforte, Peio Ibarrondo and Mikel Ispizua
2022doi: 10.3934/dcds.2022112 +[Abstract](120) +[HTML](59) +[PDF](631.63KB)
Strong global and exponential attractors for a nonlinear strongly damped hyperbolic equation
Yue Sun, Zhijian Yang and Yanxia Qu
2022doi: 10.3934/dcds.2022116 +[Abstract](90) +[HTML](68) +[PDF](402.94KB)
Dynamics and entropy of $ \mathcal{S} $-graph shifts
Travis Dillon
2022doi: 10.3934/dcds.2022117 +[Abstract](133) +[HTML](37) +[PDF](454.93KB)
Liouville type theorems for stable solutions of the weighted fractional Lane-Emden system
Hatem Hajlaoui
2022doi: 10.3934/dcds.2022118 +[Abstract](129) +[HTML](30) +[PDF](355.81KB)
Hölder continuity of solutions for a class of drift-diffusion equations
Quoc-Hung Nguyen, Yannick Sire and Le Xuan Truong
2022doi: 10.3934/dcds.2022119 +[Abstract](97) +[HTML](39) +[PDF](451.55KB)
Asymptotic lattices, good labellings, and the rotation number for quantum integrable systems
Monique Dauge, Michael A. Hall and San Vũ Ngọc
2022doi: 10.3934/dcds.2022120 +[Abstract](65) +[HTML](50) +[PDF](1364.69KB)
Diffusing orbits along chains of cylinders
Marian Gidea and Jean-Pierre Marco
2022doi: 10.3934/dcds.2022121 +[Abstract](91) +[HTML](85) +[PDF](1059.7KB)
Ground state solutions of magnetic Schrödinger equations with exponential growth
Lixi Wen, Vicentiu Rădulescu, Xianhua Tang and Sitong Chen
2022doi: 10.3934/dcds.2022122 +[Abstract](112) +[HTML](30) +[PDF](504.29KB)
$ L^2 $-Gradient flows of spectral functionals
Dario Mazzoleni and Giuseppe Savaré
2022doi: 10.3934/dcds.2022123 +[Abstract](68) +[HTML](33) +[PDF](514.82KB)
$ L^1 $–stability of vortex sheets and entropy waves in steady supersonic Euler flows over Lipschitz walls
Gui-Qiang G. Chen and Vaibhav Kukreja
2022doi: 10.3934/dcds.2022124 +[Abstract](118) +[HTML](40) +[PDF](524.41KB)
Hölder regularity for mixed local and nonlocal $ p $-Laplace parabolic equations
Bin Shang and Chao Zhang
2022doi: 10.3934/dcds.2022126 +[Abstract](113) +[HTML](28) +[PDF](382.36KB)
Generic properties of geodesic flows on analytic hypersurfaces of Euclidean space
Andrew Clarke
2022doi: 10.3934/dcds.2022127 +[Abstract](73) +[HTML](27) +[PDF](433.24KB)
Anderson localization for multi-frequency quasi-periodic Jacobi operators
Zhen Zhang and Xiong Li
2022doi: 10.3934/dcds.2022128 +[Abstract](111) +[HTML](31) +[PDF](421.55KB)
Upper and lower $ L^2 $-decay bounds for a class of derivative nonlinear Schrödinger equations
Chunhua Li, Yoshinori Nishii, Yuji Sagawa and Hideaki Sunagawa
2022doi: 10.3934/dcds.2022129 +[Abstract](111) +[HTML](45) +[PDF](393.65KB)
Infinitely many positive solutions for a class of semilinear elliptic equations
Hong-Ge Chen, Jiaojiao Zhang and Jie Zhao
2022doi: 10.3934/dcds.2022130 +[Abstract](87) +[HTML](27) +[PDF](506.62KB)
On some refraction billiards
Irene De Blasi and Susanna Terracini
2022doi: 10.3934/dcds.2022131 +[Abstract](68) +[HTML](49) +[PDF](3260.04KB)
Existence, stability and asymptotic behaviour of normalized solutions for the Davey-Stewartson system
Zhiqian He, Binhua Feng and Jiayin Liu
2022doi: 10.3934/dcds.2022132 +[Abstract](90) +[HTML](18) +[PDF](440.71KB)
On the prescribed negative Gauss curvature problem for graphs
Alessio Figalli and Christoph Kehle
2022doi: 10.3934/dcds.2022133 +[Abstract](103) +[HTML](29) +[PDF](361.58KB)
Non simple blow ups for the Nirenberg problem on half spheres
Mohameden Ahmedou and Mohamed Ben Ayed
2022doi: 10.3934/dcds.2022134 +[Abstract](12) +[HTML](6) +[PDF](518.55KB)
Maximal escape rate for shifts
Claudio Bonanno, Giampaolo Cristadoro and Marco Lenci
2022doi: 10.3934/dcds.2022135 +[Abstract](31) +[HTML](8) +[PDF](1154.7KB)
Bounds and long term convergence for the voltage-conductance kinetic system arising in neuroscience
Xu'an Dou, Benoît Perthame, Delphine Salort and Zhennan Zhou
2022doi: 10.3934/dcds.2022136 +[Abstract](6) +[HTML](2) +[PDF](346.61KB)
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](11054) +[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](7369) +[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](5586) +[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](9196) +[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](6682) +[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](8197) +[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
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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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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](11054) +[PDF](382.7KB) PDF Downloads(1349)
Differentiability of the Hartman--Grobman linearization
Misha Guysinsky, Boris Hasselblatt and Victoria Rayskin
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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](10231) +[PDF](401.1KB) PDF Downloads(1179)
Understanding Thomas-Fermi-Like approximations: Averaging over oscillating occupied orbitals
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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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On Geometric Mechanics
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2021 Impact Factor: 1.588
5 Year Impact Factor: 1.568
2021 CiteScore: 2.4

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