Asymptotic smoothing and global attractors for a class of nonlinear evolution equations (Q1952500)

Summary: We prove the asymptotic regularity of global solutions for a class of semilinear evolution equations in \(H^1_0(\Omega) \times H^1_0(\Omega)\). Moreover, we study the long-time behavior of the solutions. It is proved that, under the natural assumptions, these equations possess the compact attractor \(\mathcal A\) which is bounded in \(H^2(\Omega) \times H^2(\Omega)\), where the nonlinear term \(f\) satisfies a critical exponential growth condition.