Fractional decay bounds for nonlocal zero order heat equations. (27th June 2014) - Chasseigne, E.; Felmer, P.; Rossi, J. D.; Topp, E.
Abstract : In this paper, we obtain bounds for the decay rate for solutions to the nonlocal problem∂ t u ( t, x ) = ∫ R n J ( x, y ) [ u ( t, y ) − u ( t, x ) ] d y . Here we deal with bounded kernelsJ but with polynomial tails, that is, we assume a lower bound of the formJ ( x, y ) ⩾ c 1 | x − y | − ( n + 2 σ ), for| x − y | > c 2 . Our estimates takes the form∥ u ( t ) ∥ L q ( R n ) ⩽ C t − ( n / 2 σ ) ( 1 − 1 / q ) fort large.