More and more contributions in Environmental Economics put forward the pressing necessity of incorporating realistic representation of ecological systems to adequately tackle the sustainable development question. In this regard, it seems primordial to extend dynamic optimization models into spatial settings, as the spatial dependency is embedded in a vast array of economic and environmental problems. However, standard macroeconomics models have for long restricted their attention to time. Recently some authors have tried to extend economic models to incorporate a spatial dimension in order to describe in a more realistic manner the world's economic and environmental problems. Although encouraging, these attempts have been restricted for the main part to an abstract, essentially featureless, approach of space in one dimension, without accounting for natural and geographical factors. The aim of this master's thesis project is thus to build on the recent theoretical developments made in the spatial growth literature to study dynamic pollution management in two-dimensional stylized geographical settings, with appropriate and realistic descriptions of economic and environmental interacting systems. Focusing on the impact on health of pollution from industrial sources, we will take into account its transport and diffusion through air, soil or water to study the role of geography in the process of sustainable development and to explore the design of spatially dependent regulation in an optimal control problem. This work is thought as a combination of theoretical developments, numerical treatment and empirical applications, solving the model in typified illustrative examples as well as in the context of real world regions with polluting activities.