Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 277, pp. 1-15.
Dynamics and optimal control for a spatially-structured
environmental-economic model
Davide La Torre, Danilo Liuzzi,Tufail Malik, Oluwaseun Sharomi, Rachad Zaki
Abstract:
A deterministic model of economic growth and pollution accumulation,
in the form of a system of partial differential equations,
is designed and analyzed. The model assumes pollution as a by-product of
production. The stock of pollution has a negative impact on production.
The accumulation of pollution is dampened by a share of the investments,
in the form of an environmental tax. We consider a linear region where
both capital and pollution can diffuse. This economic-environmental
model is described by a pair of partial differential equations whose
dynamics and steady state characteristics with respect to time and
space are studied. Then we look at this ambient environment from the
point of view of a social planner who can act on the consumption and
taxation, also functions of time and space, considering the dynamics of
capital and pollution as constraints.
Submitted June 1, 2015. Published November 4, 2015.
Math Subject Classifications: 35K57, 49K20, 91B76.
Key Words: Solow model; pollution; economic growth; spatial diffusion.
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Davide La Torre
Department of Economics, Management and Quantitative Methods
University of Milan, Milan, Italy.
email: davide.latorre@unimi.it, davide.latorre@kustar.ac.ae
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Danilo Liuzzi
Department of Economics, Management and Quantitative Methods
University of Milan, Milan, Italy.
email: danilo.liuzzi@unimi.it, danilo.liuzzi@kustar.ac.ae
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Tufail Malik
Department of Applied Mathematics and Sciences
Khalifa University of Science, Technology and Research
Abu Dhabi, United Arab Emirates
email: tufail.malik@kustar.ac.ae
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Oluwaseun Sharomi
Department of Applied Mathematics and Sciences
Khalifa University of Science, Technology and Research
Abu Dhabi, United Arab Emirates
email: oluwaseun.sharomi@kustar.ac.ae
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Rachad Zaki
Department of Applied Mathematics and Sciences
Khalifa University of Science, Technology and Research
Abu Dhabi, United Arab Emirates
email: rachad.zaki@kustar.ac.ae
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