On a stable approximation to boundary value problems for evolution operator-differential equations with variable domains

Abstract

In the present paper, we introduce an approximation to linear operator-differential equations that provides well-posed solvability of boundary value problems for these equations. For the approximate solution of such problems, we suggest a method stable with respect to the input data of these problems and, in particular, with respect to the operator coefficients of the equations in the nonweakened energy inequalities. This method, which will be called the internal approximation method, can even be used to analyze the well-posedness and obtain approximate solutions of boundary value problems for variable-order partial differential equations.