This article is concerned with the existence of maximal attractors in Hi(i=1,2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conduc-tive ideal gas in bounded annular domains Ωn in Rn(n =2,3).One of the important features is that the metric spaces H(1),H(2),and H(4) we work with are three incomplete metric spaces,as can be seen from the constraints θ>0 and u>0,with θ and u being absolute temperature and specific volume respectively.For any constants δ1,δ2,···,δ8 verifying some conditions,a sequence of closed subspaces Hδ(i)H(i)(i = 1,2,4) is found,and the existence of maximal(universal) attractors in Hδ(i)(i = 1,2,4) is established.
In this paper, we shall establish some global existence results for the higherdimensional nonhomogeneous, linear, semilinear and nonlinear Thermoelastic plates with memory respectively by using semigroup approach. The existence and decay of solutions of homogeneous linear problem has been solved by Romero [1] .
In this paper, we obtain some global existence results for the higher-dimensional nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semi-group approach.
The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is presented.Then,the results are applied to non-autonomous 2D Navier-Stokes equations.
This paper is concerned with the decay rate of solutions for a quasilinear wave equation with viscosity. We use a so-called energy perturbation method to establish decay rate of solutions in terms of energy norm for a class of nonlinear functions. With the help of a comparison lemma of differential inequalities, we establish a relationship between decay rate of solutions and f .
This paper is concerned with the existence of pullback attractors for the three dimensional nonautonomous Navier-Stokes-Voight equations for the processes generated by the weak and strong solutions. The main difficulty is how to establish the pullback asymptotic compactness via energy equation approach under suitable assumption on external force.
In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua's estimate technique, we prove the decay property of energy for anisotropic elastic system.
