Cities on the Coast and Patterns of Movement between Population Growth and Diffusion

Sea level rise and high-impact coastal hazards due to on-going and projected <br>climate change dramatically affect many coastal urban areas worldwide, including those <br>with highest urbanization growth rates. To develop tailored coastal climate services that <br>can inform decision makers on climate adaptation in coastal cities, a better understanding <br>and modeling of multifaceted urban dynamics is important. We develop a coastal urban <br>model family, where the population growth and urbanization rates are modeled in the <br>framework of diffusion over the half-bounded and bounded domains, and apply the <br>maximum entropy principle to the latter case. Population density distributions are derived <br>analytically whenever possible. Steady-state wave solutions balancing the width of inhabited <br>coastal zones with the skewed distributions maximizing population entropy in them might <br>be responsible for the coast-ward migrations outstripping the demographic development <