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Solving direct and inverse problems for Fredholm-type integro-differential equations with application to pollution diffusion modeling

Author

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  • Berenguer, M.I.
  • Gámez, D.
  • Kunze, H.
  • La Torre, D.
  • Ruiz Galán, M.

Abstract

We analyze a particular Fredholm-type partial integro-differential equation. We study the direct problem and prove existence and uniqueness of the solution via a fixed-point argument for generalized contractive maps. This approach also allows us to formulate a collage-type result that can be used to solve inverse problems. We provide numerical examples and we also show how these equations can be used to model pollution diffusion of heavy pollutants and non-volatile substances such as heavy metals, chemical spills, radioactive isotopes, and others.

Suggested Citation

  • Berenguer, M.I. & Gámez, D. & Kunze, H. & La Torre, D. & Ruiz Galán, M., 2024. "Solving direct and inverse problems for Fredholm-type integro-differential equations with application to pollution diffusion modeling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 394-404.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:394-404
    DOI: 10.1016/j.matcom.2024.04.021
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    References listed on IDEAS

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    1. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    2. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2019. "Population and geography do matter for sustainable development," Environment and Development Economics, Cambridge University Press, vol. 24(2), pages 201-223, April.
    3. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics," AMSE Working Papers 1334, Aix-Marseille School of Economics, France, revised 05 Jun 2013.
    4. Vanhems, Anne, 2006. "Nonparametric Study Of Solutions Of Differential Equations," Econometric Theory, Cambridge University Press, vol. 22(1), pages 127-157, February.
    5. Xiaoyan Deng & Qingxi Liao, 2009. "Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-14, June.
    6. Davide Torre & Danilo Liuzzi & Simone Marsiglio, 2017. "Pollution Control Under Uncertainty and Sustainability Concern," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(4), pages 885-903, August.
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