Discrete and Continuous Dynamical Systems - Series A: latest papers http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=1 Latest articles for selected journal http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14728 An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14728 Carlos Matheus and Jacob Palis Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14729 Receding horizon control for the stabilization of the wave equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14729 Behzad Azmi and Karl Kunisch Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14730 Positive solutions for critically coupled Schrödinger systems with attractive interactions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14730 0$ and $\beta>0$, $-\lambda_1(\Omega)<\lambda_1,\lambda_2<0$, here $\lambda_1(\Omega)$ is the first eigenvalue of $-\Delta$ with the Dirichlet boundary condition. We give the optimal ranges of $\beta>0$ for the existence of positive solutions to the problem, which is an open problem proposed by Chen and Zou in [Arch. Rational Mech. Anal. 205 (2012), 515-551]. Finally, as a by-product of our approaches, we extend the existence results to a critically coupled Schrödinger system defined in the whole space: $$\left\{ \begin{array}{ll} -\Delta u+u=\mu_1u^{3}+ \beta uv^{2}+f(u), & \hbox{$x\in \mathbb{R}^4$}, \\ -\Delta v+v=\mu_2v^{3}+ \beta vu^{2}+g(v), & \hbox{$x\in \mathbb{R}^4$}.\\ \end{array} \right. $$ ]]> Hongyu Ye Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14731 Linear diffusion with singular absorption potential and/or unbounded convective flow: The weighted space approach http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14731 Jesus Ildefonso Díaz, David Gómez-Castro, Jean Michel Rakotoson and Roger Temam Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14732 Nonradial least energy solutions of the $p$-Laplace elliptic equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14732 Ryuji Kajikiya Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14733 Energy-critical NLS with potentials of quadratic growth http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14733     We closely follow the previous concentration compactness arguments for the harmonic oscillator. A key technical difference is that in the absence of a concrete formula for the linear propagator, we apply more general tools from microlocal analysis, including a Fourier integral parametrix of Fujiwara. ]]> Casey Jao Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14734 Bounded and unbounded capillary surfaces derived from the catenoid http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14734 Filippo Morabito Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14735 On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14735 0, i,j=1,\cdots,n, $$ which is the classical Atkson-Allen map when $r_i=1$ and $c_i=c$ for all $i=1,...,n$ and a discretized system of the competitive Lotka-Volterra equations. It is proved that every $n$-dimensional map $T$ of this form admits a carrying simplex $\Sigma$ which is a globally attracting invariant hypersurface of codimension one. We define an equivalence relation relative to local stability of fixed points on the boundary of $\Sigma$ on the space of all such three-dimensional maps. In the three-dimensional case we list a total of $33$ stable equivalence classes and draw the corresponding phase portraits on each $\Sigma$. The dynamics of the generalized competitive Atkinson-Allen map differs from the dynamics of the standard one in that Neimark-Sacker bifurcations occur in two classes for which no such bifurcations were possible for the standard competitive Atkinson-Allen map. We also found Chenciner bifurcations by numerical examples which implies that two invariant closed curves can coexist for this model, whereas those have not yet been found for all other three-dimensional competitive mappings via the carrying simplex. In one class every map admits a heteroclinic cycle; we provide a stability criterion for heteroclinic cycles. Besides, the generalized Atkinson-Allen model is not dynamically consistent with the Lotka-Volterra system. ]]> Mats Gyllenberg, Jifa Jiang, Lei Niu and Ping Yan Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14736 On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14736 Messoud Efendiev and Anna Zhigun Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14737 Nonexistence results for elliptic differential inequalities with a potential in bounded domains http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14737 Dario D. Monticelli and Fabio Punzo Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14738 Nonlinear Schrödinger equations on periodic metric graphs http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14738 Alexander Pankov Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14739 The continuum limit of Follow-the-Leader models --- a short proof http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14739 Helge Holden and Nils Henrik Risebro Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14740 On uniqueness of measure-valued solutions to Liouville's equation of Hamiltonian PDEs http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14740 Ammari Zied and Liard Quentin Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14741 Dispersive effects of weakly compressible and fast rotating inviscid fluids http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14741 5/2 $. We prove that the system admits a unique local strong solution in $ L^\infty \left( [0,T]; H^s\left( \mathbb{R}^3 \right) \right) $, where $ T $ is independent of the Rossby and Mach numbers. Moreover, using Strichartz-type estimates, we prove the longtime existence of the solution, i.e. its lifespan is of the order of $\varepsilon^{-\alpha}, \alpha >0$, without any smallness assumption on the initial data (the initial data can even go to infinity in some sense), provided that the rotation is fast enough. ]]> Van-Sang Ngo and Stefano Scrobogna Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14742 N-barrier maximum principle for degenerate elliptic systems and its application http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14742 Chiun-Chuan Chen, Li-Chang Hung and Hsiao-Feng Liu Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14743 A Liouville-type theorem for cooperative parabolic systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14743 0$, $p=r+s+1$. The real matrix $A=(a_{ij})$ satisfies conditions $ a_{12}, a_{21}\geq 0$ and $a_{11}, a_{22}>0$. This paper is a continuation of Phan-Souplet (Math. Ann., 366, 1561-1585, 2016) where the authors considered the special case $s=r$ for the system of $m$ components. Our tool for the proof of Liouville-type theorem is a refinement of Phan-Souplet, which is based on Gidas-Spruck (Commun. Pure Appl.Math. 34, 525--598 1981) and Bidaut-Véron (Équations aux dérivées partielles et applications. Elsevier, Paris, pp 189--198, 1998). ]]> Anh Tuan Duong and Quoc Hung Phan Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14744 Reversing and extended symmetries of shift spaces http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14744 extended symmetries. We develop their basic theory for faithful $\mathbb{Z}^{d}$-actions, and determine the extended symmetry group of the chair tiling shift, which can be described as a model set, and of Ledrappier's shift, which is an example of algebraic origin. ]]> Michael Baake, John A. G. Roberts and Reem Yassawi Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14745 A robustly transitive diffeomorphism of Kan's type http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14745 Cheng Cheng, Shaobo Gan and Yi Shi Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14746 Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14746 Anna Cima, Armengol Gasull and Víctor Mañosa Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14747 Propagation phenomena for CNNs with asymmetric templates and distributed delays http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14747 0$. Especially, if cells possess the symmetric templates and the same delayed interactions, then $c_{-}^*=c_{+}^*>0$. Moreover, if the effect of the self-feedback interaction $\alpha f'(0)$ is not less than 1, then both $c_{-}^*>0$ and $c_{+}^*>0$. For the non-monotone case, the leftward and rightward spreading speeds are investigated by combining the theory of the spreading speed for the monotone case and squeezing the given output function between two appropriate nondecreasing functions. It turns out that the leftward and rightward spreading speeds are linearly determinate in these two cases. We further obtain the existence and nonexistence of travelling wave solutions under the weaker conditions than those in [46,47] and show that the spreading speed coincides with the minimal wave speed. ]]> Zhixian Yu and Xiaoqiang Zhao Thu, 1 Feb 2018 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14748 Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14748 Antonio Pumariño, José Ángel Rodríguez and Enrique Vigil Thu, 1 Feb 2018 08:00:00 GMT