Difference inequalities generated by impulsive parabolic differential-functional problems

The paper deals with parabolic differential-functional equations. Initial-boundary value problems are considered with impulses given in fixed points. We prove theorems on difference-functional impulsive inequalities generated by original problems. it finite difference schemes are used to approximate the solutions of the original problems. We give sufficient conditions for the convergence of sequences of approximate solutions under the assumptions that the right-hand sides satisfy the nonlinear estimates of the Perron type with respect to the functional argument. In proof of the convergence of difference methods we apply theorems on difference-functional impulsive inequalities.