Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel [PDF]
, 2007 We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions.
Fucci, Guglielmo +2 more
core +2 more sources
Attractors of multivalued semiflows generated by differential inclusions and their approximations
Abstract and Applied Analysis, Volume 5, Issue 1, Page 33-46, 2000., 2000 We prove the existence of global compact attractors for differential inclusions and obtain some results concerning the continuity and upper semicontinuity of the attractors for approximating and perturbed inclusions. Applications are given to a model of regional economic growth.
Alexei V. Kapustian, José Valero
wiley +1 more source
On the strongly damped wave equation and the heat equation with mixed boundary conditions
Abstract and Applied Analysis, Volume 5, Issue 3, Page 175-189, 2000., 2000 We study two one‐dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
Aloisio F. Neves
wiley +1 more source
Open Mathematics, 2019 We first introduce the concept of the random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system (NRDS) and give a theorem on the existence of the random uniform exponential attractor for a jointly continuous ...
Han Zongfei, Zhou Shengfan
doaj +1 more source
Asymptotic behaviour of the non-autonomous 3D Navier-Stokes problem with coercive force [PDF]
, 2010 We construct pullback attractors to the weak solutions of the three-dimensional Dirichlet problem for the incompressible Navier-Stokes equations in the case when the external force may become unbounded as time goes to plus or minus infinity.Comment: 22 ...
Vorotnikov, Dmitry
core +2 more sources
A condition on delay for differential equations with discrete state-dependent delay [PDF]
, 2010 Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V.
Alexander V. Rezounenko +43 more
core +2 more sources
Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent [PDF]
, 2011 In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega) and then it is proved ...
A. Kh. Khanmamedov +22 more
core +1 more source
Asymptotics of the Coleman-Gurtin model [PDF]
, 2010 This paper is concerned with the integrodifferential equation $$\partial_t u-\Delta u -\int_0^\infty \kappa(s)\Delta u(t-s)\,\d s + \varphi(u)=f$$ arising in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in presence of a ...
Chekroun, Mickaël D. +3 more
core +1 more source
Attractors for processes on time-dependent spaces. Applications to wave equations [PDF]
, 2012 For a process U(t,s) acting on a one-parameter family of normed spaces, we present a notion of time-dependent attractor based only on the minimality with respect to the pullback attraction property. Such an attractor is shown to be invariant whenever the
Conti, Monica +2 more
core +1 more source
Global attractors for the one dimensional wave equation with displacement dependent damping
, 2010 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 global ...
Arrietta +10 more
core +1 more source