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This paper is concerned with the lifetime maximisation of wireless sensor networks (WSNs) in the context of slow-fading communication channels. The problem is first formulated as a decomposable convex optimisation problem. Dual decomposition is presented as a way to decompose the problem into smaller subproblems that can be solved locally by the nodes. Particular attention is paid to networks using cooperative communication techniques. As illustrative examples, formulations of the network lifetime maximisation problem are provided in the presence of (i) single-relay cooperation and (ii) broadcast-cooperative beamforming operations exploiting the spacial diversity of WSNs.