Abstract
ABSTRACT We study the two‐dimensional Cauchy–Dirichlet problems for the quasilinear pseudoparabolic integro‐differential Volterra equation and for the quasilinear pseudoparabolic integro‐differential Fredholm equation. In each of these two problems, the integral term depends on a positive integer parameter and, as , converges weakly to the expression incorporating the Dirac delta‐function, which models an instantaneous impulsive impact. For fixed we prove the well‐posedness of each of the two problems in the class of regular weak solutions. Further, for each of the two problems, we establish that the initial shock layer, associated with the Dirac delta‐function, is formed as , and that the family of regular weak solutions of the original problem converges to the strong solution of a limit two‐scale microscopic–macroscopic model.