Related papers: Time-Dependent Attractor for the Oscillon Equation
We study spacetimes that lead to a separable Klein-Gordon equation in a general dimension. We introduce an ansatz for the metric in higher dimensions motivated by analogical work by Carter in four dimensions and find solutions of the…
This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive…
In this paper we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.
This work is focused on the dissipative system describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of the temperature. Under natural boundary…
This paper concerns the tempered pullback dynamics of 2D incompressible non-autonomous Navier-Stokes equation with non-homogeneous boundary condition on Lipschitz-like domain. With the presence of a time-dependent external force f(t) which…
We consider a two-dimensional nonstationary Navier-Stokes shear flow with a subdifferential boundary condition on a part of the boundary of the flow domain, namely, with a boundary driving subject to the Tresca law. There exists a unique…
We investigate the time-evolution problem associated with the Klein-Gordon equation, using superoscillations as initial data. Additionally, the Segal-Bargmann transform is used to derive integral representations of the resulting solutions.
We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously…
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges…
The main objective of this paper is to investigate exponential attractors for a nonlocal delayed reaction-diffusion equation on an unbounded domain. We first obtain the existence of a globally attractive absorbing set for the dynamical…
The implications of manifestly covariant formulation of relativistic quantum mechanics depending on a scalar evolution parameter, canonically conjugated to the variable mass, is still an unsettled issue. In this work we find a complete set…
The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infinite interval with a Dirichlet boundary condition on the…
In this paper we investigate a class of nonautonomous linear parabolic problems with time depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic…
We consider the asymptotic behavior of solutions to the Cauchy problem for the defocusing nonlinear Klein-Gordon equation (NLKG) with exponential nonlinearity in the one spatial dimension with data in the energy space $H^1(\mathbb{R})…
This note complements the paper \cite{LP} by proving a scattering statement for solutions of nonlinear Klein-Gordon equations with an internal mode in $3$d. We show that small solutions exhibit growth around a one-dimensional set in…
We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force,…
In this paper, the existence, uniqueness, and positivity of solutions, as well as the asymptotic behavior through a finite fractal dimensional global attractor for a general Advection-Diffusion-Reaction (ADR) equation, are investigated. Our…
The main objective of this paper is to study the existence of a finite dimension global attractor for the three dimensional viscous primitive equations of large-scale atmosphere. Thanks to the shortage of the uniqueness of weak solutions,…
In this paper we study the effects of a ``nonlocal'' term on the global dynamics of the Kuramoto-Sivashinsky equation. We show that the equation possesses a ``family of maximal attractors'' parameterized by the mean value of the initial…
By introducing the scalar potential as modification in the mass term of the Klein-Gordon equation, the influence of a Coulomb-type potential on the Klein-Gordon oscillator is investigated. Relativistic bound states solutions are achieved to…