Boundary Value Problems for Degenerating and Nondegenerating Sobolev-Type Equations with a Nonlocal Source in Differential and Difference Forms

Abstract

Boundary value problems are considered for degenerating and nondegenerating differential equations of the Sobolev type with a nonlocal source as well as finite-difference methods for solving these problems. A priori estimates are derived for solving the problems posed in differential and difference interpretations. These a priori estimates entail the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer as well as the convergence of the solution of each difference problem to that of the counterpart differential problem.