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.
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, 223, 394-404 [10.1016/j.matcom.2024.04.021].
Solving direct and inverse problems for Fredholm-type integro-differential equations with application to pollution diffusion modeling
La Torre, D.;
2024
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
