Related papers: Exponential attractor for the viscoelastic wave mo…
A time-dependent determining wavenumber was introduced in [5] to estimate the number of determining modes for the surface quasi-geostrophic (SQG) equation. In this paper we continue this investigation focusing on the subcritical case and…
Disordered stealthy hyperuniform dielectric composites exhibit novel electromagnetic wave transport properties in two and three dimensions. Here, we carry out the first study of the electromagnetic properties of one-dimensional (1D)…
Hydrodynamic attractors have recently gained prominence in the context of early stages of ultra-relativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of…
We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…
We consider the inverse problem of determining a time-dependent damping coefficient $a$ and a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+a(t,x)\partial_tu+q(t,x)u=0$ in $Q=(0,T)\times\Omega$, with…
We perform direct numerical simulations of the tidal encounter of a rotating planet on a highly eccentric or parabolic orbit about a central star formulated as an initial value problem. This approach enables us to extend previous work of…
In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subjects to periodic boundary conditions. More exactly, the linear wave equation $u_{tt}-u_{xx}+Mu+\varepsilon…
We show that a simple non-linear system of ordinary differential equations may possess a time varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We…
This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a…
The possibility of linking inflation and late cosmic accelerated expansion using the $\alpha$-attractor models has received increasing attention due to their physical motivation. In the early universe, $\alpha$-attractors provide an…
In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the…
We study the mechanism of decay of a topological (winding-number) excitation due to finite-size effects in a two-dimensional valence-bond solid state, realized in an $S=1/2$ spin model ($J$-$Q$ model) and studied using projector Monte Carlo…
We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate $1:1$ or $1:-1$ semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite…
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a…
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…
Throughout the literature on Neural Cellular Automata (NCAs), it is often taken for granted that the systems learn attractors. This is shown through evolving the system for many timesteps and noting visual similarity to the goal state.…
We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…
Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…
We consider a model for the evolution of a mixture of two incompressible and partially immiscible Newtonian fluids in two dimensional bounded domain. More precisely, we address the well-known model H consisting of the Navier-Stokes equation…
The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form $(-\Delta)^\alpha\partial_t u$, $\alpha\in(0,\frac{1}{2})$, in bounded smooth domains of $\Bbb R^3$. It appears that to…