Discrete & Continuous Dynamical Systems
August 2021 , Volume 41 , Issue 8
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We obtain some Hölder regularity estimates for an Hamilton-Jacobi with fractional time derivative of order
In this paper, we construct center stable manifolds around unstable line solitary waves of the Zakharov–Kuznetsov equation on two dimensional cylindrical spaces
We consider the barotropic Navier–Stokes system describing the motion of a compressible Newtonian fluid in a bounded domain with in and out flux boundary conditions. We show that if the boundary velocity coincides with that of a rigid motion, all solutions converge to an equilibrium state for large times.
We consider a homoclinic orbit to a saddle fixed point of an arbitrary
In this paper, we study the multiplicity of two spikes nodal solutions for a nonautonomous Schrödinger–Poisson system with the nonlinearity
We prove the existence of bounded and periodic solutions for planar systems by introducing a notion of lower and upper solutions which generalizes the classical one for scalar second order equations. The proof relies on phase plane analysis; after suitably modifying the nonlinearities, the Ważewski theory provides a solution which remains bounded in the future. For the periodic problem, the Massera Theorem applies, yielding the existence result. We then show how our result generalizes some well known theorems on the existence of bounded and of periodic solutions. Finally, we provide some corollaries on the existence of almost periodic solutions for scalar second order equations.
We characterize proximality of multidimensional
We extend the result of Yan to Broucke's isosceles orbit with masses
We present a definition of chaotic Delone set and establish the genericity of chaos in the space of
The notions of fair measure and fair entropy were introduced by Misiurewicz and Rodrigues [
In this paper we study the scattering of radial solutions to a
In this paper, we establish a convergence result for the operator splitting scheme
Suppose a set of prototiles allows
We resume the investigation, started in [
We study the complex-valued modified Korteweg-de Vries equation (mKdV) on the circle. We first consider the real-valued setting and show global well-posedness of the (usual) renormalized mKdV equation in the Fourier-Lebesgue spaces. In the complex-valued setting, we observe that the momentum plays an important role in the well-posedness theory. In particular, we prove that the complex-valued mKdV equation is ill-posed in the sense of non-existence of solutions when the momentum is infinite, in the spirit of the work on the nonlinear Schrödinger equation by Guo-Oh (2018). This non-existence result motivates the introduction of the second renormalized mKdV equation, which we propose as the correct model in the complex-valued setting outside
We consider the existence of response solutions for the quasi-periodic perturbation of degenerate reversible harmonic oscillators
In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, 3d cubic NLS, and 2d quintic NLS (nonlinear Schrödinger equations).
In this paper, we study the equilibria of an anisotropic, nonlocal aggregation equation with nonlinear diffusion which does not possess a gradient flow structure. Here, the anisotropy is induced by an underlying tensor field. Anisotropic forces cannot be associated with a potential in general and stationary solutions of anisotropic aggregation equations generally cannot be regarded as minimizers of an energy functional. We derive equilibrium conditions for stationary line patterns in the setting of spatially homogeneous tensor fields. The stationary solutions can be regarded as the minimizers of a regularised energy functional depending on a scalar potential. A dimension reduction from the two- to the one-dimensional setting allows us to study the associated one-dimensional problem instead of the two-dimensional setting. We establish
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