In MIP (Mobile IP) a Home Agent (HA) allocates the IP address and when the mobile device changes geographic area the Foreign Agent (FA) may provide a mobile specific "care of address" (CoA) to the HA so that packets can be forwarded to the correct destination where the mobile happens to be located. These functionalities are supported in LTE at the home P-GW which acts as the HA and the S-GW which can act as FA when mobile IP is used.
