About One Problem for the MAC Model for the Heat Conduction Equation

The aim of this work is to study a class of problems for continuum models in mechanics. We construct the MAC model for the parabolic equation which could include the physical solution appying Newton’s law of cooling. A notion of a generalized solution is introduced. We apply Galerkin method to prove the existence of a generalized solution. The proof of uniqueness of a generalized solution is based on the obtained energy inequality.