On some systems of partial differential equations with a small parameter in the principal part

In this paper, we examine systems of partial differential equations containing a small positive parameter in the principal part. We establish a relationship between solutions of the system with a small parameter and solutions of the limit system obtained if the parameter is equal to zero. We present classes of systems that preserve the properties of regularly perturbed problems under singular perturbations are admit constructing asymptotic solutions by methods of regular perturbation theory.