Dynamics and regularity for non-autonomous reaction-diffusion equations with anomalous diffusion

This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in L-2(ohm) and H-0(alpha) (ohm) (0 < alpha < 1) have been achieved with a restriction on the growth order of nonlinearity as 2 <= p <= 2(n-alpha)|n 2 alpha. The results presented can be seen as the extension for classical theory of infinite dimensional dynamical system to the fractional diffusion equations. This paper is concerned with the long time behavior of solutions for a non-autonomous reaction-diffusion equations with anomalous diffusion. Under suitable assumptions on nonlinearity and external force, the global well-posedness has been studied. Then the pullback attractors in L-2(Omega) and H-0(alpha) (Omega) (0 < alpha < 1) have been achieved with a restriction on the growth order of nonlinearity as 2 <= p <= 2(n-alpha a) n-2a. The results presented can be seen as the extension for classical theory of infinite dimensional dynamical system to the fractional diffusion equations.