This paper is concerned with longtime dynamics of semilinear Lamé systems $$\begin{aligned} \partial ^2_t u - \mu \Delta (\lambda + ) \nabla \mathrm{div} \alpha _t f(u) = b, \end{aligned}$$ defined in bounded domains $${\mathbb {R}}^3$$ Dirichlet boundary condition. Firstly, we establish the existence finite dimensional global attractors subjected to a critical forcing f(u). Writing $$\lambda $...

In the present paper we study the weak lower semicontinuity of the functional

This paper is devoted to introduce an axiomatic model to distinguish what functions are suitable for measuring the degree of contradiction between two Atanassov’s intuitionistic fuzzy sets. After stating the needed background, in section 2, we justify and present the axioms that a contradiction measure must satisfy, and the first examples are set out. After motivating the necessity of achieving...

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. will establish the value function under total variation, setwise, and weak convergence structures. Our analysis reveals that for bounded is continuous variation structures in both zero-sum games team problems. Continuity ...

In this work, we discuss the large time behaviour of solutions two-dimensional stochastic convective Brinkman–Forchheimer (SCBF) equations on bounded domains. Under functional setting V?H?V?, where H and V are appropriate separable Hilbert spaces fact that embedding V?H is compact, establish existence random attractors in for flow generated by 2D SCBF perturbed additive noise. We prove upper se...

The aim of this paper is to study the long-time dynamics solutions evolution system { u t ? ? + ? ( ) 1 2 a ? v = f , x ? ? × ? ? 0 subject boundary conditions ? where bounded smooth domain in R n ? 3 with ?? assumed be regular enough, > constant, Hölder continuous function and dissipative nonlinearity. This problem non-autonomous version well known Klein-Gordon-Zakharov system. Using uniform s...

The paper investigates some continuity properties of pullback and exponential attractors the non-autonomous problem Form II Mindlin's strain gradient viscoelastic plate derived recently by Aouadi [2]. Under quite general assumptions on nonlinear damping sources terms, we establish existence uniqueness weak strong solutions. We prove in natural space energy, its upper semicontinuity with respect...

Suppose a given evolutionary equation has a compact attractor and the evolutionary equation is approximated by a finite-dimensional system. Conditions are given to ensure the approximate system has a compact attractor which converges to the original one as the approximation is refined. Applications are given to parabolic and hyperbolic partial differential equations.