Galaxy clusters are promising targets for indirect dark matter searches .
Gamma-ray signatures from the decay or annihilation of dark matter particles inside these clusters could be observable with the Fermi Large Area Telescope ( LAT ) .
Based on three years of Fermi LAT gamma-ray data , we analyze the flux coming from eight nearby clusters individually as well as in a combined likelihood analysis .
Concentrating mostly on signals from dark matter decay , we take into account uncertainties of the cluster masses as determined by X-ray observations and model the cluster emission as extended sources .
Searching for different hadronic and leptonic decay and annihilation spectra , we do not find significant emission from any of the considered clusters and present limits on the dark matter lifetime and annihilation cross-section .
We compare our lifetime limits derived from cluster observations with the limits that can be obtained from the extragalactic gamma-ray background ( EGBG ) , and find that in case of hadronic decay the cluster limits become competitive at dark matter masses below a few hundred GeV .
In case of leptonic decay , however , galaxy cluster limits are stronger than the limits from the EGBG over the full considered mass range .
Finally , we show that in presence of dark matter substructures down to 10 ^ { -6 } solar masses the limits on the dark matter annihilation cross-section could improve by a factor of a few hundred , possibly going down to the thermal cross-section of 3 \times 10 ^ { -26 } \text { cm } ^ { 3 } s ^ { -1 } for dark matter masses \lesssim 150 \text { GeV } and annihilation into b \bar { b } .
As a direct application of our results , we derive limits on the lifetime of gravitino dark matter in scenarios with R -parity violation .
Implications of these limits for the possible observation of long-lived superparticles at the LHC are discussed .