Attractors for a class of doubly nonlinear parabolic systems

Abstract

In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $\left[ L^{\infty }(\Omega )\right] ^{2}$ and ${\prod_{i=1}^{2}}{B_{\infty }^{1+\sigma_{i},p_{i}}( \Omega )} $.