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.

We study stochastic partly dissipative lattice systems with random coupled coefficients and multiplicative/additive white noise in a weighted space of infinite sequences. We first show that these stochastic partly dissipative lattice differential equations generate a random dynamical system. We then establish the existence of a tempered random bounded absorbing set and a global compact random a...

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.