Asymptotic behavior of reaction-diffusion equations with time-dependent advection term

In this paper, we study the long-time dynamics of a reaction-diffusion population model incorporating time-dependent nonlinear advection term. We address the technical challenges arising from the nonlinear advection term, which results in the lack of uniqueness of weak solutions. This, in turn, leads to a multivalued nonautonomous dynamical system. We establish the existence of minimal pullback attractors within universes of bounded and tempered sets and examine the relationships between these attractors. Furthermore, by considering the advective term defined by an $ \varepsilon $-family of coefficients, we prove the upper semicontinuity of the pullback attractors with respect to the parameter $ \varepsilon $.