REGULARITY OF GLOBAL ATTRACTORS FOR REACTION-DIFFUSION SYSTEMS WITH NO MORE THAN QUADRATIC GROWTH

摘要

We consider reaction-diffusion systems in a three-dimensional bounded domain under standard dissipativity conditions and quadratic growth conditions. No smoothness or monotonicity conditions are assumed. We prove that every weak solution is regular and use this fact to show that the global attractor of the corresponding multi-valued semiflow is compact in the space (H_0~1(Ω))~N.