Sea level rise and high-impact coastal hazards due to on-going and projected climate change dramatically affect many coastal urban areas worldwide, including those with the highest urbanization growth rates. To develop tailored coastal climate services that can inform decision makers on climate adaptation in coastal cities, a better understanding and modeling of multifaceted urban dynamics is important. We develop a coastal urban model family, where the population growth and urbanization rates are modeled in the framework of diffusion over the half-bounded and bounded domains, and apply the maximum entropy principle to the latter case. Population density distributions are derived analytically whenever possible. Steady-state wave solutions balancing the width of inhabited coastal zones, with the skewed distributions maximizing population entropy, might be responsible for the coastward migrations outstripping the demographic development of the hinterland. With appropriate modifications of boundary conditions, the developed family of diffusion models can describe coastal urban dynamics affected by climate change.
Open AccessArticle Cities on the Coast and Patterns of Movement between Population Growth and Diffusion by Dmitry V. Kovalevsky 1,* [ORCID] , Dimitri Volchenkov 2 [ORCID] and Jürgen Scheffran 3 [ORCID] 1 Climate Service Center Germany (GERICS), Helmholtz-Zentrum Hereon, Fischertwiete 1, 20095 Hamburg, Germany 2 Department of Mathematics and Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA 3 Research Group Climate Change and Security (CLISEC), Institute of Geography, Center for Earth System Research and Sustainability (CEN), Universität Hamburg, Grindelberg 7, 20144 Hamburg, Germany * Author to whom correspondence should be addressed. Academic Editor: Karsten Keller Entropy 2021, 23(8), 1041; https://doi.org/10.3390/e23081041 Received: 29 June 2021 / Revised: 7 August 2021 / Accepted: 9 August 2021 / Published: 13 August 2021 (This article belongs to the Special Issue Mathematical Analysis of Urban Spatial Networks) Download PDF Browse Figures Citation Export Abstract Sea level rise and high-impact coastal hazards due to on-going and projected climate change dramatically affect many coastal urban areas worldwide, including those with the highest urbanization growth rates. To develop tailored coastal climate services that can inform decision makers on climate adaptation in coastal cities, a better understanding and modeling of multifaceted urban dynamics is important. We develop a coastal urban model family, where the population growth and urbanization rates are modeled in the framework of diffusion over the half-bounded and bounded domains, and apply the maximum entropy principle to the latter case. Population density distributions are derived analytically whenever possible. Steady-state wave solutions balancing the width of inhabited coastal zones, with the skewed distributions maximizing population entropy, might be responsible for the coastward migrations outstripping the demographic development of the hinterland. With appropriate modifications of boundary conditions, the developed family of diffusion models can describe coastal urban dynamics affected by climate change.