1D Impulsive Pseudoparabolic Equation with Convection and Absorption

We study the 1D initial-boundary value problem for the pseudoparabolic equation with a nonlinear convection term and a linear absorption term. The absorption term depends on a positive integer parameter $n$ and, as $n\to+\infty$, converges weakly$^\star$ to the expression incorporating the Dirac delta function, which models an instant absorption at the initial moment of time. We prove that the infinitesimal initial layer, associated with the Dirac delta function, is formed as $n\to+\infty$, and that the family of regular weak solutions of the original problem converges to the strong solution of a two-scale microscopic-macroscopic model. The main novelty of the article consists of taking into account of the effect of convection.