About One Problem for the MAC Model for the Heat Conduction Equation
Olga Danilkina *
Department of Mathematics, College of Natural and Mathematical Sciences, the University of Dodoma, P.O.BOX 259, Dodoma, Tanzania.
Igor Neygebauer
Department of Mathematics, College of Natural and Mathematical Sciences, the University of Dodoma, P.O.BOX 259, Dodoma, Tanzania.
Geminipeter Augustino Lyakurwa
Department of Mathematics, College of Natural and Mathematical Sciences, the University of Dodoma, P.O.BOX 259, Dodoma, Tanzania.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Parabolic equations, MAC model, apriori estimate, loaded equations.