ASYMPTOTIC EXPANSIONS OF SOLUTIONS OF FRACTIONAL DIFFUSION EQUATIONS

In this paper we obtain the precise description of the asymptotic behavior of the solution u of the fractional diffusion equation partial derivative(t)u + (-Delta)(theta/2) u = 0 in R-N x (0,infinity) with the initial data phi is an element of L-K := L-1(R-N, (1 + |x|)(K) dx), where 0 < theta < 2 and K >= 0. This enables us to obtain the asymptotic behavior of the hot spots of the solution u. Furthermore, we develop the arguments in [K. Ishige and T. Kawakami, Math. Ann., 353 (2012), pp. 161-192] and [K. Ishige, T. Kawakami, and K. Kobayashi, J. Evol. Equ., 14 (2014), pp. 749-777] and establish a method to obtain the asymptotic expansions of the solutions to inhomogeneous fractional diffusion equations and nonlinear fractional diffusion equations.