A theoretical study for air pollution model as‎ a free boundary ‎problem‎

This paper presents a theoretical investigation of an air pollution model formulated as a free boundary problem‎. ‎The study examines the dynamics of pollutant dispersion in the atmosphere‎, ‎where the boundaries of the polluted region are not fixed but evolve over time‎. ‎Using advanced mathematical techniques and partial differential equations‎, ‎we construct a model that accounts for various factors influencing air pollution‎, ‎including emission sources‎, ‎meteorological conditions‎, ‎and chemical reactions‎. ‎The incorporation of a free boundary framework provides a more realistic representation of pollutant spread and environmental interactions‎. ‎To analyze the model‎, ‎we employ the Friedman-Rubinstein integral representation method and apply the Banach contraction theorem to solve an equivalent nonlinear Volterra integral equation

Keywords:

Air ‎pollution , ‎ free boundary ‎problem , ‎ Volterra’s integral ‎equations , ‎‎ Green’s ‎function