At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

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...

‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...

This paper is concerned with the asymptotic behavior of solutions to nonlocal stochastic partial differential equations multiplicative and additive noise driven by a standard Brownian motion, respectively. First all, are transformed into their associated conjugated random equations, we then construct dynamical systems original problems via properties conjugation. Next, in case noise, establish ...