Segmentation is a core strategy in modern marketing and age-specific segmentation, which is based on the age of the consumers, is very common in practice. A characteristic of age-specific segmentation is the change of the segments composition during time, which may be studied only using dynamic advertising models. Here, we assume that a firm wants to promote and sell a single product in an age segmented market and we model the awareness of this product using an infinite dimensional Nerlove- Arrow goodwill as a state variable. Assuming an infinite time horizon, we use some dynamic programming techniques to solve the problem and to characterize both the optimal advertising effort and the optimal goodwill path in the long run. An interesting feature of the optimal advertising effort is an anticipation effect with respect to the segments considered in the target market due to the time evolution of the segmentation.Segmentation; infinite dimensional Nerlove-Arrow goodwill.