2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139908We study a class of quadratic, infinite-dimensional dynamical systems, inspired by models for viscoelastic fluids. We prove that these equations define a semi-flow on the cone of positive, essentially bounded functions. As time tends to infinity, the solutions tend to an equilibrium manifold in the $L^2$-norm. Convergence to a particular function on the equilibrium manifold is only proved under additional assumptions. We discuss several possible generalizations.Dynamical SystemsAnalysis of PDEs35F25, 37C70, 35Q72.text