Related papers: On attractors for a sharp interface model of exoth…
We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…
We establish the effective {\em finite dimensionality} of the dynamics corresponding to a flow-plate interaction PDE model arising in aeroelasticity: a nonlinear panel, in the absence of rotational inertia, immersed in an inviscid potential…
A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of $\R^N$. Under the assumption that the obstacle $\K$ is a closed convex and bounded subset of $\mathbb{R}^n$ with smooth boundary or it is a closed…
In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < $\alpha$ < 1. We turn the free interface problem…
The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…
We investigate the cosmological attractor of the minimally coupled, self-interacting phantom field with a positive energy density but negative pressure. It is proved that the phantom cosmology is rigid in the sense that there exists a…
Cosmological simulations of dark matter structures have identified a set of universal profiles, and similar characteristics have been seen in non-cosmological simulations. It has therefore been speculated whether these profiles of…
We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…
In this paper we study the fractal dimension of global attractors for a class of wave equations with (single-point) degenerate nonlocal damping. Both the equation and its linearization degenerate into linear wave equations at the degenerate…
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as…
We clarify the connection between attractor solutions known from studies of Bjorken flow in conformal models of relativistic fluid dynamics and the more general description of attractors as submanifolds in phase space. We show how to…
In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the…
Under general boundary conditions we consider the finiteness of the Hausdorff and fractal dimensions of the global attractor for the strong solution of the 3D moist primitive equations with viscosity. Firstly, we obtain time-uniform…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
We consider the limit of a linear kinetic equation, with reflection-transmission-absorption at an interface, with a degenerate scattering kernel. The equation arise from a microscopic chain of oscillators in contact with a heat bath. In the…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
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,…
We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann-Robertson-Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton-Jacobi…
We study the mechanical contact between a deformable body with a wavy surface and a rigid flat taking into account pressurized fluid trapped in the interface. A finite element model is formulated for a general problem of trapped fluid for…
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different…