Vietnam Journal of Mathematics

, Volume 45, Issue 1–2, pp 199–206 | Cite as

Optimizing Environmental Taxation on Physical Capital for a Spatially Structured Economic Growth Model Including Pollution Diffusion

  • Sebastian AniţaEmail author
  • Vincenzo Capasso
  • Herb Kunze
  • Davide La Torre


We present a spatially structured dynamic economic growth model which takes into account the level of pollution induced by production, and a possible taxation based on the amount of produced pollution. Then we analyze an optimal harvesting control problem with an objective function composed of three terms, namely the intertemporal utility of the decision maker, the space-time average of the level of pollution in the habitat, and the disutility due to the imposition of taxation. With respect to our previous works, in this paper, the system is subject to two controls, namely the level of consumption and, in addition, the taxation on physical capital rate. The optimal controls are determined by means of a sweep-type numerical algorithm that allows to solve a system of four backward-forward reaction-diffusion equations.


Reaction-diffusion systems Integral nonlocal term Large-time behavior Control problems Economic growth Environmental quality Taxation Convex-concave production function 

Mathematics Subject Classification (2010)

35K57 35Q91 93D15 49K20 91B62 91B76 



The work of S. Aniţa was supported by a grant of the Romanian Ministry of National Education, CNCS-UEFISCDI, project number PN-II-ID-PCE-2012-4-0270 (68/2.09.2013): “Optimal Control and Stabilization of Nonlinear Parabolic Systems with State Constraints. Applications in Life Sciences and Economics”. The work by V. Capasso has been supported by a Chair of Excellence at the Universidad Carlos III de Madrid.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  • Sebastian Aniţa
    • 1
    Email author
  • Vincenzo Capasso
    • 2
  • Herb Kunze
    • 3
  • Davide La Torre
    • 4
    • 5
  1. 1.Faculty of Mathematics“Al.I. Cuza” University of Iaşi and “Octav Mayer” Institute of MathematicsIaşiRomania
  2. 2.Department of MathematicsUniversity of MilanMilanItaly
  3. 3.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada
  4. 4.Department of Economics, Management, and Quantitative MethodsUniversity of MilanMilanItaly
  5. 5.Department of Applied Mathematics and SciencesKhalifa UniversityAbu DhabiUnited Arab Emirates

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