:. J. Aknowledgements, was partially supported by MEC MTM2010- 18128 and MTM2011-27998 (Spain) and FONDECYT 1110291 International Coperation. P.F. was partially supported by FONDECYT 1110291 and Programa Basal-CMM U. de Chile, E.T. was partially supported by CONICYT

F. Andreu-vaillo, J. M. Mazon, J. D. Rossi, and J. J. Toledo-melero, Nonlocal diffusion problems, Mathematical Surveys and Monographs, vol.165, 2010.
DOI : 10.1090/surv/165

E. Chasseigne, M. Chaves, and J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.3, pp.271-291, 2006.
DOI : 10.1016/j.matpur.2006.04.005

D. Neza, E. Palatucci, G. Valdinoci, and E. , Hitchhiker??s guide to the fractional Sobolev spaces, Bulletin des Sciences Math??matiques, vol.136, issue.5, pp.521-573, 2012.
DOI : 10.1016/j.bulsci.2011.12.004

L. Ignat and J. D. Rossi, Decay estimates for nonlocal problems via energy methods, Journal de Math??matiques Pures et Appliqu??es, vol.92, issue.2, pp.163-187, 2009.
DOI : 10.1016/j.matpur.2009.04.009

. France, Chasseigne@lmpt.univ-tours.fr Patricio Felmer: Departamento de Ingeniería Matemática and CMM (UMI 2807 CNRS), Buenos Aires, Argentina. julio.rossi@ua.es Erwin Topp: Departamento de Ingeniería Matemática, 1428.