Discrete and Continuous Dynamical Systems
May 2021 , Volume 41 , Issue 5
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We consider a minimal equicontinuous action of a finitely generated group
The Cauchy problem of the modified Camassa-Holm (mCH) equation with initial data
We consider a class
In this paper, applying the Maslov-type index theory for periodic orbits and brake orbits, we study the minimal period problems in asymptotically linear Hamiltonian systems with different symmetries. For the asymptotically linear semipositive even Hamiltonian systems, we prove that for any given
In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover some known results for the behavior of the eigenvalues of the
We study the norm potentials of Hölder continuous
We are concerned with the radially symmetric stationary wave for the exterior problem of two-dimensional Burgers equation. A sufficient and necessary condition to guarantee the existence of such a stationary wave is given and it is also shown that the stationary wave satisfies nice decay estimates and is time-asymptotically nonlinear stable under radially symmetric initial perturbation.
Moreover, we prove that the solution of (1) is
The celebrated result of Eskin, Margulis and Mozes [
The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in
In this paper, we first establish decay estimates for the fractional and higher-order fractional Hénon-Lane-Emden systems by using a nonlocal average and integral estimates, which deduce a result of non-existence. Next, we apply the method of scaling spheres introduced in [
In this paper, we consider the uniformly elliptic nonlocal operators
In this paper we study solutions of the stationary Navier-Stokes system, and investigate the minimal decay rate for a nontrivial velocity field at infinity in outside of an obstacle. We prove that in an exterior domain if a solution
We consider a
It has been proved in [
uniformly converges, for
It is known that the time-one mapping of a flow defines a discrete dynamical system with the same dynamical behaviors as the flow, but conversely one wants to know whether a flow embedded by a homeomorphism preserves the dynamical behaviors of the homeomorphism. In this paper we consider iterative roots, a weak version of embedded flows, for the preservation. We refer an iterative root to be genetic if it is topologically conjugate to its parent function. We prove that none of PM functions with height being
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power type nonlinearity, stability and instability for standing wave solutions have been extensively studied. On the other hand, in the case of our system, there are no results concerning the stability and instability as far as we know.
In this paper, we prove strong blow-up instability for the standing wave to our system. The proof is based on the techniques in Ohta and Todorova [
In this paper we extend the notions of sample and Euler stabilizability to a set of a control system to a wide class of systems with unbounded controls, which includes nonlinear control-polynomial systems. In particular, we allow discontinuous stabilizing feedbacks, which are unbounded approaching the target. As a consequence, sampling trajectories may present a chattering behaviour and Euler solutions have in general an impulsive character. We also associate to the control system a cost and provide sufficient conditions, based on the existence of a special Lyapunov function, which allow for the existence of a stabilizing feedback that keeps the cost of all sampling and Euler solutions starting from the same point below the same value, in a uniform way.
The Novikov equation is an integrable Camassa-Holm type equation with cubic nonlinearity. One of the most important features of this equation is the existence of peakon and multi-peakon solutions, i.e. peaked traveling waves behaving as solitons. This paper aims to prove both, the orbital and asymptotic stability of peakon trains solutions, i.e. multi-peakon solutions such that their initial configuration is increasingly ordered. Furthermore, we give an improvement of the orbital stability of a single peakon so that we can drop the non-negativity hypothesis on the momentum density. The same result also holds for the orbital stability for peakon trains, i.e. in this latter case we can also avoid assuming non-negativity of the initial momentum density. Finally, as a corollary of these results together with some asymptotic formulas for the position and momenta vectors for multi-peakon solutions, we obtain the orbital and asymptotic stability for initially not well-ordered multipeakons.
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