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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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Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators
Thomas Kappeler and Riccardo Montalto
2022, 42(9) : 4127-4201 doi: 10.3934/dcds.2022048 +[Abstract](163) +[HTML](104) +[PDF](697.39KB)
The Neumann problem for a class of mixed complex Hessian equations
Chuanqiang Chen, Li Chen, Xinqun Mei and Ni Xiang
2022, 42(9) : 4203-4218 doi: 10.3934/dcds.2022049 +[Abstract](202) +[HTML](63) +[PDF](347.15KB)
Mean dimension theory in symbolic dynamics for finitely generated amenable groups
Yunping Wang, Ercai Chen and Xiaoyao Zhou
2022, 42(9) : 4219-4236 doi: 10.3934/dcds.2022050 +[Abstract](157) +[HTML](65) +[PDF](361.67KB)
Achievable connectivities of Fatou components for a family of singular perturbations
Jordi Canela, Xavier Jarque and Dan Paraschiv
2022, 42(9) : 4237-4261 doi: 10.3934/dcds.2022051 +[Abstract](143) +[HTML](53) +[PDF](1546.41KB)
An upper bound of the measure-theoretical entropy
Yuntao Zang
2022, 42(9) : 4263-4295 doi: 10.3934/dcds.2022052 +[Abstract](145) +[HTML](57) +[PDF](676.4KB)
Instability results for the logarithmic Sobolev inequality and its application to related inequalities
Daesung Kim
2022, 42(9) : 4297-4320 doi: 10.3934/dcds.2022053 +[Abstract](160) +[HTML](54) +[PDF](478.17KB)
The topology of Bott integrable fluids
Robert Cardona
2022, 42(9) : 4321-4345 doi: 10.3934/dcds.2022054 +[Abstract](209) +[HTML](100) +[PDF](629.91KB)
Limit theorems for higher rank actions on Heisenberg nilmanifolds
Minsung Kim
2022, 42(9) : 4347-4383 doi: 10.3934/dcds.2022057 +[Abstract](190) +[HTML](49) +[PDF](568.8KB)
Global existence and blow up for systems of nonlinear wave equations related to the weak null condition
Kunio Hidano and Kazuyoshi Yokoyama
2022, 42(9) : 4385-4414 doi: 10.3934/dcds.2022058 +[Abstract](139) +[HTML](57) +[PDF](433.28KB)
Critical gauged Schrödinger equations in $ \mathbb{R}^2 $ with vanishing potentials
Liejun Shen, Marco Squassina and Minbo Yang
2022, 42(9) : 4415-4438 doi: 10.3934/dcds.2022059 +[Abstract](161) +[HTML](49) +[PDF](449.37KB)
Long-time asymptotics for the modified complex short pulse equation
Mingming Chen, Xianguo Geng and Kedong Wang
2022, 42(9) : 4439-4470 doi: 10.3934/dcds.2022060 +[Abstract](202) +[HTML](84) +[PDF](481.41KB)
Comparison principles for nonlocal Hamilton-Jacobi equations
Gonzalo Dávila
2022, 42(9) : 4471-4488 doi: 10.3934/dcds.2022061 +[Abstract](167) +[HTML](46) +[PDF](328.48KB)
Global existence of weak solutions for the 3D axisymmetric chemotaxis-Navier-Stokes equations with nonlinear diffusion
Xiaoyu Chen, Jijie Zhao and Qian Zhang
2022, 42(9) : 4489-4522 doi: 10.3934/dcds.2022062 +[Abstract](192) +[HTML](61) +[PDF](436.98KB)
Global well-posedness of 2D incompressible Magnetohydrodynamic equations with horizontal dissipation
Xiaoxiao Suo and Quansen Jiu
2022, 42(9) : 4523-4553 doi: 10.3934/dcds.2022063 +[Abstract](103) +[HTML](42) +[PDF](362.77KB)
Invariant tori for the derivative nonlinear Schrödinger equation with nonlinear term depending on spatial variable
Zhaowei Lou, Jianguo Si and Shimin Wang
2022, 42(9) : 4555-4595 doi: 10.3934/dcds.2022064 +[Abstract](106) +[HTML](44) +[PDF](533.91KB)
Bismut formula for intrinsic/Lions derivatives of distribution dependent SDEs with singular coefficients
Xing Huang, Yulin Song and Feng-Yu Wang
2022, 42(9) : 4597-4614 doi: 10.3934/dcds.2022065 +[Abstract](107) +[HTML](36) +[PDF](369.42KB)
Global well-posedness of the Cauchy problem for the Jordan–Moore–Gibson–Thompson equation with arbitrarily large higher-order Sobolev norms
Belkacem Said-Houari
2022, 42(9) : 4615-4635 doi: 10.3934/dcds.2022066 +[Abstract](200) +[HTML](44) +[PDF](344.68KB)
Multiple ergodic averages for variable polynomials
Andreas Koutsogiannis
2022, 42(9) : 4637-4668 doi: 10.3934/dcds.2022067 +[Abstract](141) +[HTML](40) +[PDF](499.26KB)
A game theoretical approximation for a parabolic/elliptic system with different operators
Alfredo Miranda and Julio D. Rossi
2022doi: 10.3934/dcds.2022034 +[Abstract](179) +[HTML](79) +[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](174) +[HTML](101) +[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](159) +[HTML](63) +[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](146) +[HTML](53) +[PDF](317.18KB)
Elliptic systems with nonlinear diffusion and a convection term
Lucio Boccardo and Luigi Orsina
2022doi: 10.3934/dcds.2022056 +[Abstract](166) +[HTML](54) +[PDF](353.88KB)
Positive solutions to a nonlinear fractional equation with an external source term
Qi Li, Kefan Pan and Shuangjie Peng
2022doi: 10.3934/dcds.2022068 +[Abstract](119) +[HTML](51) +[PDF](465.11KB)
Asymptotic behavior of spreading fronts in an anisotropic multi-stable equation on $ \mathit{\boldsymbol{\mathbb{R}^N}} $
Hiroshi Matsuzawa and Mitsunori Nara
2022doi: 10.3934/dcds.2022069 +[Abstract](129) +[HTML](73) +[PDF](484.99KB)
Classifications of positive solutions to an integral system involving the multilinear fractional integral inequality
Huaiyu Zhou and Jingbo Dou
2022doi: 10.3934/dcds.2022070 +[Abstract](99) +[HTML](33) +[PDF](449.91KB)
On a nonhomogeneous Kirchhoff type elliptic system with the singular Trudinger-Moser growth
Shengbing Deng and Xingliang Tian
2022doi: 10.3934/dcds.2022071 +[Abstract](147) +[HTML](35) +[PDF](456.89KB)
Topological characterizations of Morse-Smale flows on surfaces and generic non-Morse-Smale flows
Vladislav Kibkalo and Tomoo Yokoyama
2022doi: 10.3934/dcds.2022072 +[Abstract](97) +[HTML](35) +[PDF](764.29KB)
Statistical properties of type D dispersing billiards
Margaret Brown and Péter Nándori
2022doi: 10.3934/dcds.2022073 +[Abstract](56) +[HTML](20) +[PDF](480.83KB)
Existence of invariant curves for degenerate almost periodic reversible mappings
Peng Huang
2022doi: 10.3934/dcds.2022074 +[Abstract](69) +[HTML](24) +[PDF](445.82KB)
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](81) +[HTML](32) +[PDF](602.15KB)
Symmetrization for fractional nonlinear elliptic problems
Vincenzo Ferone and Bruno Volzone
2022doi: 10.3934/dcds.2022076 +[Abstract](79) +[HTML](25) +[PDF](479.12KB)
On the asymptotic behavior of solutions for the self-dual Maxwell-Chern-Simons $ O(3) $ Sigma model
Zhi-You Chen, Chung-Yang Wang and Yu-Jen Huang
2022doi: 10.3934/dcds.2022077 +[Abstract](69) +[HTML](46) +[PDF](371.82KB)
Zero-diffusion limit for aggregation equations over bounded domains
Razvan C. Fetecau, Hui Huang, Daniel Messenger and Weiran Sun
2022doi: 10.3934/dcds.2022078 +[Abstract](69) +[HTML](17) +[PDF](1662.52KB)
Large time behavior for a nonlocal nonlinear gradient flow
Feng Li and Erik Lindgren
2022doi: 10.3934/dcds.2022079 +[Abstract](63) +[HTML](17) +[PDF](461.19KB)
Parabolic methods for ultraspherical interpolation inequalities
Jean Dolbeault and An Zhang
2022doi: 10.3934/dcds.2022080 +[Abstract](59) +[HTML](17) +[PDF](452.78KB)
On multi-solitons for coupled Lowest Landau Level equations
Laurent Thomann
2022doi: 10.3934/dcds.2022081 +[Abstract](35) +[HTML](13) +[PDF](412.9KB)
Iterative roots of type $ \mathcal {T}_2 $
Liu Liu, Justyna Jarczyk, Witold Jarczyk and Weinian Zhang
2022doi: 10.3934/dcds.2022082 +[Abstract](53) +[HTML](17) +[PDF](526.72KB)
Boundary concentrations on segments for a Neumann Ambrosetti-Prodi problem
Weiwei Ao, Mengdie Fu and Chao Liu
2022doi: 10.3934/dcds.2022083 +[Abstract](42) +[HTML](12) +[PDF](400.08KB)
An optimization problem in heat conduction with volume constraint and double obstacles
Xiaoliang Li and Cong Wang
2022doi: 10.3934/dcds.2022084 +[Abstract](47) +[HTML](15) +[PDF](387.66KB)
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](10500) +[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](6971) +[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](5260) +[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](8947) +[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](6519) +[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](7997) +[PDF](246.2KB) Cited By(198)
Partial regularity of the dynamic system modeling the flow of liquid crystals
Fanghua Lin and Chun Liu
1996, 2(1) : 1-22 doi: 10.3934/dcds.1996.2.1 +[Abstract](4717) +[PDF](222.9KB) Cited By(170)
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](7699) +[PDF](369.4KB) Cited By(169)
Remarks on regularities for the 3D MHD equations
Yong Zhou
2005, 12(5) : 881-886 doi: 10.3934/dcds.2005.12.881 +[Abstract](5391) +[PDF](176.3KB) Cited By(168)
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](9781) +[PDF](401.1KB) Cited By(155)
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](7699) +[PDF](369.4KB) PDF Downloads(2381)
Some questions looking for answers in dynamical systems
Carles Simó
2018, 38(12) : 6215-6239 doi: 10.3934/dcds.2018267 +[Abstract](6438) +[HTML](373) +[PDF](531.03KB) PDF Downloads(2063)
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](2600) +[HTML](168) +[PDF](370.02KB) PDF Downloads(1911)
Conditional measures and conditional expectation; Rohlin's Disintegration Theorem
David Simmons
2012, 32(7) : 2565-2582 doi: 10.3934/dcds.2012.32.2565 +[Abstract](4631) +[PDF](444.9KB) PDF Downloads(1708)
Differentiability of the Hartman--Grobman linearization
Misha Guysinsky, Boris Hasselblatt and Victoria Rayskin
2003, 9(4) : 979-984 doi: 10.3934/dcds.2003.9.979 +[Abstract](3308) +[PDF](131.0KB) PDF Downloads(1265)
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](10500) +[PDF](382.7KB) PDF Downloads(1197)
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](9781) +[PDF](401.1KB) PDF Downloads(1094)
Understanding Thomas-Fermi-Like approximations: Averaging over oscillating occupied orbitals
John P. Perdew and Adrienn Ruzsinszky
2013, 33(11&12) : 5319-5325 doi: 10.3934/dcds.2013.33.5319 +[Abstract](2664) +[PDF](258.5KB) PDF Downloads(1037)
On the spectral theory of positive operators and PDE applications
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2020, 40(6) : 3171-3200 doi: 10.3934/dcds.2020054 +[Abstract](2953) +[HTML](915) +[PDF](460.48KB) PDF Downloads(1028)
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2021 Impact Factor: 1.588
5 Year Impact Factor: 1.568
2021 CiteScore: 2.4

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