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In this paper, we address the problem of energy efficiency in ad hoc wireless networks. We consider a network that is shared by a set of sources, each one communicating with its corresponding destination using multiple routes. Each source is associated with a utility function which increases with the total traffic flowing over the available source-destination routes. The network lifetime is defined as the time until the first node in the network runs out of energy. We formulate the problem as one of maximizing the sum of the sources' utilities subject to the required constraint on network lifetime. We present a primal formulation of the problem, which uses penalty functions to take into account the system constraints, and we introduce a new methodology for solving the problem. The proposed approach leads to a flow control algorithm, which provides the optimal sources' rate and can be easily implemented in a distributed manner. When compared with the minimum transmission energy routing scheme, the proposed algorithm gives significantly higher sources' rates for same network lifetime guarantee.