摘要
The paper first discusses the longtime behavior of the activator-inhibitor model, the existence of the maximal attractor is given. Then using the mathematical induction and the properties of linear semigroup, the regularity result for the maximal attractor is obtained. Next, it is proved that its Hausdorff or fractal dimension is finite.Finally, further estimates are verilied by Rothe’s inequality and fractional operators, and the existence of inertial manifold is then proved.
The paper first discusses the longtime behavior of the activator-inhibitor model, the existence of the maximal attractor is given. Then using the mathematical induction and the properties of linear semigroup, the regularity result for the maximal attractor is obtained. Next, it is proved that its Hausdorff or fractal dimension is finite.Finally, further estimates are verilied by Rothe's inequality and fractional operators, and the existence of inertial manifold is then proved.
