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AIMS joins the mathematics community worldwide in congratulating ProfessorAlessio Figalli on being awarded the Fields Medal 2018. Professor Figallihas made important contributions to AIMS journals and conferences. Heserved as the Managing Editor of Discrete and Continuous Dynamical Systemsfrom 2012 to 2016 and delivered a plenary lecture at the 11th AIMSconference (2016) in Orlando, USA. Details can be found at

Congratulations, Alessio!

DCDS, series A 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.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 12 issues a year, monthly.
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  • Archived in Portico and CLOCKSS.
  • DCDS is a publication of the American Institute of Mathematical Sciences. All rights reserved.

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Propagation of long-crested water waves. Ⅱ. Bore propagation
Jerry L. Bona, Thierry Colin and Colette Guillopé
2019, 39(10) : 5543-5569 doi: 10.3934/dcds.2019244 +[Abstract](365) +[HTML](144) +[PDF](387.71KB)
Reflected solutions of backward doubly SDEs driven by Brownian motion and Poisson random measure
Monia Karouf
2019, 39(10) : 5571-5601 doi: 10.3934/dcds.2019245 +[Abstract](335) +[HTML](78) +[PDF](480.81KB)
Standing and travelling waves in a parabolic-hyperbolic system
Michiel Bertsch, Hirofumi Izuhara, Masayasu Mimura and Tohru Wakasa
2019, 39(10) : 5603-5635 doi: 10.3934/dcds.2019246 +[Abstract](344) +[HTML](99) +[PDF](1505.07KB)
A semidiscrete scheme for evolution equations with memory
Filippo Dell'Oro, Olivier Goubet, Youcef Mammeri and Vittorino Pata
2019, 39(10) : 5637-5658 doi: 10.3934/dcds.2019247 +[Abstract](304) +[HTML](81) +[PDF](393.32KB)
Slices of parameter spaces of generalized Nevanlinna functions
Tao Chen and Linda Keen
2019, 39(10) : 5659-5681 doi: 10.3934/dcds.2019248 +[Abstract](162) +[HTML](85) +[PDF](540.2KB)
Dynamical behavior of a multigroup SIRS epidemic model with standard incidence rates and Markovian switching
Qun Liu, Daqing Jiang, Tasawar Hayat and Ahmed Alsaedi
2019, 39(10) : 5683-5706 doi: 10.3934/dcds.2019249 +[Abstract](176) +[HTML](104) +[PDF](409.81KB)
An operator splitting scheme for the fractional kinetic Fokker-Planck equation
Manh Hong Duong and Yulong Lu
2019, 39(10) : 5707-5727 doi: 10.3934/dcds.2019250 +[Abstract](182) +[HTML](55) +[PDF](421.13KB)
On the maximal saddle order of $ p:-q $ resonant saddle
Guangfeng Dong, Changjian Liu and Jiazhong Yang
2019, 39(10) : 5729-5742 doi: 10.3934/dcds.2019251 +[Abstract](143) +[HTML](65) +[PDF](358.31KB)
Product of expansive Markov maps with hole
Haritha C and Nikita Agarwal
2019, 39(10) : 5743-5774 doi: 10.3934/dcds.2019252 +[Abstract](188) +[HTML](76) +[PDF](1847.29KB)
On a resonant and superlinear elliptic system
Fabiana Maria Ferreira and Francisco Odair de Paiva
2019, 39(10) : 5775-5784 doi: 10.3934/dcds.2019253 +[Abstract](170) +[HTML](64) +[PDF](284.61KB)
Variational proof of the existence of brake orbits in the planar 2-center problem
Yuika Kajihara and Misturu Shibayama
2019, 39(10) : 5785-5797 doi: 10.3934/dcds.2019254 +[Abstract](159) +[HTML](77) +[PDF](154.94KB)
Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations
Abraham Solar
2019, 39(10) : 5799-5823 doi: 10.3934/dcds.2019255 +[Abstract](215) +[HTML](93) +[PDF](505.35KB)
Sign-changing solutions for some nonhomogeneous nonlocal critical elliptic problems
Salomón Alarcón and Jinggang Tan
2019, 39(10) : 5825-5846 doi: 10.3934/dcds.2019256 +[Abstract](213) +[HTML](100) +[PDF](428.19KB)
Uniqueness and nondegeneracy of solutions for a critical nonlocal equation
Lele Du and Minbo Yang
2019, 39(10) : 5847-5866 doi: 10.3934/dcds.2019219 +[Abstract](174) +[HTML](91) +[PDF](425.56KB)
Ground state solutions of Nehari-Pohozaev type for the planar Schrödinger-Poisson system with general nonlinearity
Sitong Chen, Junping Shi and Xianhua Tang
2019, 39(10) : 5867-5889 doi: 10.3934/dcds.2019257 +[Abstract](230) +[HTML](132) +[PDF](426.56KB)
Multiplicative combinatorial properties of return time sets in minimal dynamical systems
Daniel Glasscock, Andreas Koutsogiannis and Florian Karl Richter
2019, 39(10) : 5891-5921 doi: 10.3934/dcds.2019258 +[Abstract](149) +[HTML](70) +[PDF](477.6KB)
The nonlinear Schrödinger equations with harmonic potential in modulation spaces
Divyang G. Bhimani
2019, 39(10) : 5923-5944 doi: 10.3934/dcds.2019259 +[Abstract](144) +[HTML](70) +[PDF](434.93KB)
Traveling waves of a full parabolic attraction-repulsion chemotaxis system with logistic source
Rachidi B. Salako
2019, 39(10) : 5945-5973 doi: 10.3934/dcds.2019260 +[Abstract](148) +[HTML](64) +[PDF](495.06KB)
Robust attractors for a perturbed non-autonomous extensible beam equation with nonlinear nonlocal damping
Yanan Li, Zhijian Yang and Fang Da
2019, 39(10) : 5975-6000 doi: 10.3934/dcds.2019261 +[Abstract](152) +[HTML](66) +[PDF](454.01KB)
On the isomorphism problem for non-minimal transformations with discrete spectrum
Nikolai Edeko
2019, 39(10) : 6001-6021 doi: 10.3934/dcds.2019262 +[Abstract](166) +[HTML](59) +[PDF](376.98KB)
Local-in-space blow-up criteria for two-component nonlinear dispersive wave system
Vural Bayrak, Emil Novruzov and Ibrahim Ozkol
2019, 39(10) : 6023-6037 doi: 10.3934/dcds.2019263 +[Abstract](202) +[HTML](83) +[PDF](372.26KB)
Weighted elliptic estimates for a mixed boundary system related to the Dirichlet-Neumann operator on a corner domain
Mei Ming
2019, 39(10) : 6039-6067 doi: 10.3934/dcds.2019264 +[Abstract](139) +[HTML](58) +[PDF](464.16KB)
Infinitely many segregated solutions for coupled nonlinear Schrödinger systems
Lushun Wang, Minbo Yang and Yu Zheng
2019, 39(10) : 6069-6102 doi: 10.3934/dcds.2019265 +[Abstract](181) +[HTML](84) +[PDF](457.81KB)
Standing waves for Schrödinger-Poisson system with general nonlinearity
Zhi Chen, Xianhua Tang, Ning Zhang and Jian Zhang
2019, 39(10) : 6103-6129 doi: 10.3934/dcds.2019266 +[Abstract](226) +[HTML](92) +[PDF](431.97KB)
Accelerating dynamical peakons and their behaviour
Stephen C. Anco and Elena Recio
2019, 39(10) : 6131-6148 doi: 10.3934/dcds.2019267 +[Abstract](144) +[HTML](67) +[PDF](531.21KB)
Sign-changing bubble-tower solutions to fractional semilinear elliptic problems
Gabriele Cora and Alessandro Iacopetti
2019, 39(10) : 6149-6173 doi: 10.3934/dcds.2019268 +[Abstract](171) +[HTML](69) +[PDF](446.36KB)
A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic fisher kpp equation
Michiel Bertsch, Danielle Hilhorst, Hirofumi Izuhara, Masayasu Mimura and Tohru Wakasa
2019doi: 10.3934/dcds.2019226 +[Abstract](410) +[HTML](161) +[PDF](479.3KB)
Cauchy problem of semilinear inhomogeneous elliptic equations of Matukuma-type with multiple growth terms
Yunfeng Jia, Yi Li, Jianhua Wu and Hong-Kun Xu
2019doi: 10.3934/dcds.2019227 +[Abstract](328) +[HTML](141) +[PDF](399.3KB)
Nondegeneracy of harmonic maps from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $
Guoyuan Chen, Yong Liu and Juncheng Wei
2019doi: 10.3934/dcds.2019228 +[Abstract](309) +[HTML](137) +[PDF](370.56KB)
Large time behavior of ODE type solutions to nonlinear diffusion equations
Junyong Eom and Kazuhiro Ishige
2019doi: 10.3934/dcds.2019229 +[Abstract](339) +[HTML](133) +[PDF](359.7KB)
Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature
Tianwen Luo, Tao Tao and Liqun Zhang
2019doi: 10.3934/dcds.2019230 +[Abstract](282) +[HTML](138) +[PDF](431.74KB)
Minimizers of the $ p $-oscillation functional
Annalisa Cesaroni, Serena Dipierro, Matteo Novaga and Enrico Valdinoci
2019doi: 10.3934/dcds.2019231 +[Abstract](279) +[HTML](138) +[PDF](307.34KB)
Superfluids passing an obstacle and vortex nucleation
Fanghua Lin and Juncheng Wei
2019doi: 10.3934/dcds.2019232 +[Abstract](264) +[HTML](146) +[PDF](444.76KB)
Free boundary problems associated with cancer treatment by combination therapy
Avner Friedman and Xiulan Lai
2019doi: 10.3934/dcds.2019233 +[Abstract](333) +[HTML](136) +[PDF](427.96KB)
Homogenization of the boundary value for the Dirichlet problem
Sunghan Kim, Ki-Ahm Lee and Henrik Shahgholian
2019doi: 10.3934/dcds.2019234 +[Abstract](317) +[HTML](149) +[PDF](444.4KB)
Regularity results for the equation $ u_{11}u_{22} = 1 $
Connor Mooney and Ovidiu Savin
2019doi: 10.3934/dcds.2019235 +[Abstract](259) +[HTML](129) +[PDF](309.52KB)
Soap films with gravity and almost-minimal surfaces
Francesco Maggi, Salvatore Stuvard and Antonello Scardicchio
2019doi: 10.3934/dcds.2019236 +[Abstract](315) +[HTML](164) +[PDF](631.82KB)
Blow-up for the 3-dimensional axially symmetric harmonic map flow into $ S^2 $
Juan Dávila, Manuel Del Pino, Catalina Pesce and Juncheng Wei
2019doi: 10.3934/dcds.2019237 +[Abstract](273) +[HTML](135) +[PDF](431.04KB)
On global solutions to semilinear elliptic equations related to the one-phase free boundary problem
Xavier Fernández-Real and Xavier Ros-Oton
2019doi: 10.3934/dcds.2019238 +[Abstract](302) +[HTML](137) +[PDF](434.59KB)
Recent progresses on elliptic two-phase free boundary problems
Daniela De Silva, Fausto Ferrari and Sandro Salsa
2019doi: 10.3934/dcds.2019239 +[Abstract](296) +[HTML](172) +[PDF](347.91KB)
The method of energy channels for nonlinear wave equations
Carlos E. Kenig
2019doi: 10.3934/dcds.2019240 +[Abstract](366) +[HTML](211) +[PDF](358.72KB)
A nondegeneracy condition for a semilinear elliptic system and the existence of 1- bump solutions
Piero Montecchiari and Paul H. Rabinowitz
2019doi: 10.3934/dcds.2019241 +[Abstract](307) +[HTML](181) +[PDF](405.55KB)
Remarks on some minimization problems associated with BV norms
Haïm Brezis
2019doi: 10.3934/dcds.2019242 +[Abstract](398) +[HTML](156) +[PDF](182.92KB)
The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals
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2019doi: 10.3934/dcds.2019243 +[Abstract](295) +[HTML](143) +[PDF](409.0KB)
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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Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
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Remarks on regularities for the 3D MHD equations
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Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
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The problem Of blow-up in nonlinear parabolic equations
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Positive solution for a nonlinear stationary Schrödinger-Poisson system in $R^3$
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BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity
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Global stability for damped Timoshenko systems
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Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces
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Regularity and classification of solutions to static Hartree equations involving fractional Laplacians
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Traveling wave solutions of a highly nonlinear shallow water equation
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Some questions looking for answers in dynamical systems
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On the universality of the incompressible Euler equation on compact manifolds
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Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus
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Classification for positive solutions of degenerate elliptic system
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The two membranes problem for fully nonlinear operators
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Weakly mixing diffeomorphisms preserving a measurable Riemannian metric with prescribed Liouville rotation behavior
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2018  Impact Factor: 1.143




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