
ISSN:
1078-0947
eISSN:
1553-5231
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Discrete and Continuous Dynamical Systems
February 2020 , Volume 40 , Issue 2
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This work focuses on stochastic systems of weakly interacting particles containing different populations represented by multi-classes. The dynamics of each particle depends not only on the empirical measure of the whole population but also on those of different populations. The limits of such systems as the number of particles tends to infinity are investigated. We establish the existence, uniqueness, and basic properties of solutions to the limiting McKean-Vlasov equations of these systems and then obtain the rate of convergence of the sequences of empirical measures associated with the systems to their limits in terms of the
We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on
The dynamics is studied of an infinite collection of point particles placed in
We consider the family of CIFSs of generalized complex continued fractions with a complex parameter space. This is a new interesting example to which we can apply a general theory of infinite CIFSs and analytic families of infinite CIFSs. We show that the Hausdorff dimension function of the family of the CIFSs of generalized complex continued fractions is continuous in the parameter space and is real-analytic and subharmonic in the interior of the parameter space. As a corollary of these results, we also show that the Hausdorff dimension function has a maximum point and the maximum point belongs to the boundary of the parameter space.
We develop a thermodynamic formalism for a class of diffeomorphisms of a torus that are "almost-Anosov". In particular, we use a Young tower construction to prove the existence and uniqueness of equilibrium states for a collection of non-Hölder continuous geometric potentials over almost Anosov systems with an indifferent fixed point, as well as prove exponential decay of correlations and the central limit theorem for these equilibrium measures.
This paper is concerned with the multiplicity and concentration behavior of nontrivial solutions for the following fractional Kirchhoff equation in presence of a magnetic field:
where
We investigate the existence of a curve
where
In this paper, we investigate a sharp Moser-Trudinger inequality which involves the anisotropic Sobolev norm in unbounded domains. Under this anisotropic Sobolev norm, we establish the Lions type concentration-compactness alternative firstly. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality. In particular, we combine the low dimension case of
This paper introduces the concept of average conformal hyperbolic sets, which admit only one positive and one negative Lyapunov exponents for any ergodic measure. For an average conformal hyperbolic set of a
We investigate the diffusion-aggregation equations with degenerate diffusion
We study global properties of positive radial solutions of
We show that for Sturm-Liouville Systems on the half-line
The existence of singular limit solutions are investigated by establishing a new Liouville type theorem for nonlinear elliptic system by using the Pohozaev type identity and the nonlinear domain decomposition method.
We estimate the frequency of polynomial iterations which fall in a given multiplicative subgroup of a finite field of
We study the classification and evolution of bifurcation curves of positive solutions of the one-dimensional Dirichlet-Neumann problem with a specific cubic nonlinearity given by
where
The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. In this first part of the series, we investigate the dynamical behaviors of logistic type chemotaxis models on the half line
Combining fixed point techniques with the method of lower-upper solutions we prove the existence of at least one weak solution for the following boundary value problem
where
This paper is concerned with the following problem involving critical Sobolev exponent and polyharmonic operator:
where
We prove global-in-time existence and uniqueness of measure solutions of a nonlocal interaction system of two species in one spatial dimension. For initial data including atomic parts we provide a notion of gradient-flow solutions in terms of the pseudo-inverses of the corresponding cumulative distribution functions, for which the system can be stated as a gradient flow on the Hilbert space
We prove some new Liouville-type theorems for stable radial solutions of
where
2021
Impact Factor: 1.588
5 Year Impact Factor: 1.568
2021 CiteScore: 2.4
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