Global Weak Solutions for the 1D Pollutant Transport Model: The Case of ε = 0 (Contemporary Mathematics, 2025)
This paper investigates the existence of global weak solutions for a one-dimensional pollutant transport model. The study builds upon the previous work. Our primary advancement involves demonstrating that the global weak solutions of a model studied in previous work remain valid when the coefficient associated with the regularizing term is eliminated (ε = 0). To achieve this, we have refined certain a priori estimates, ensuring they are independent of the parameter ε.
Keywords: shallow water equations; bilayer models; approximate solutions; pollutant transport model