Discrete and Continuous Dynamical Systems - Series A: latest papers
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Latest articles for selected journalhttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14728
An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes
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Carlos Matheus and Jacob PalisThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14729
Receding horizon control for the stabilization of the wave equation
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Behzad Azmi and Karl KunischThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14730
Positive solutions for critically coupled Schrödinger systems with attractive interactions
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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:
$$\left\{
\begin{array}{ll}
-\Delta u+u=\mu_1u^{3}+
\beta uv^{2}+f(u), & \hbox{$x\in \mathbb{R}^4$}, \\
-\Delta v+v=\mu_2v^{3}+
\beta vu^{2}+g(v), & \hbox{$x\in \mathbb{R}^4$}.\\
\end{array}
\right.
$$
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Hongyu YeThu, 1 Feb 2018 08:00:00 GMThttp://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
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Jesus Ildefonso Díaz, David Gómez-Castro, Jean Michel Rakotoson and Roger TemamThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14732
Nonradial least energy solutions of the $p$-Laplace elliptic equations
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Ryuji KajikiyaThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14733
Energy-critical NLS with potentials of quadratic growth
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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.
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Casey JaoThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14734
Bounded and unbounded capillary surfaces derived from the catenoid
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Filippo MorabitoThu, 1 Feb 2018 08:00:00 GMThttp://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
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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.
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Mats Gyllenberg, Jifa Jiang, Lei Niu and Ping YanThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14736
On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis
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Messoud Efendiev and Anna ZhigunThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14737
Nonexistence results for elliptic differential inequalities with a potential in bounded domains
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Dario D. Monticelli and Fabio PunzoThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14738
Nonlinear Schrödinger equations on periodic metric graphs
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Alexander PankovThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14739
The continuum limit of Follow-the-Leader models --- a short proof
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Helge Holden and Nils Henrik RisebroThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14740
On uniqueness of measure-valued solutions to Liouville's equation of Hamiltonian PDEs
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Ammari Zied and Liard QuentinThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14741
Dispersive effects of weakly compressible and fast rotating inviscid fluids
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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.
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Van-Sang Ngo and Stefano ScrobognaThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14742
N-barrier maximum principle for degenerate elliptic systems and its application
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Chiun-Chuan Chen, Li-Chang Hung and Hsiao-Feng LiuThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14743
A Liouville-type theorem for cooperative parabolic systems
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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).
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Anh Tuan Duong and Quoc Hung PhanThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14744
Reversing and extended symmetries of shift spaces
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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.
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Michael Baake, John A. G. Roberts and Reem YassawiThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14745
A robustly transitive diffeomorphism of Kan's type
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Cheng Cheng, Shaobo Gan and Yi ShiThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14746
Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points
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Anna Cima, Armengol Gasull and Víctor MañosaThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14747
Propagation phenomena for CNNs with asymmetric templates and distributed delays
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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.
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Zhixian Yu and Xiaoqiang ZhaoThu, 1 Feb 2018 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14748
Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors
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Antonio Pumariño, José Ángel Rodríguez and Enrique VigilThu, 1 Feb 2018 08:00:00 GMT