The Maximum Principle of Pontryagin in the Heat-mass Transfer Problem

Abstract

A flow of a viscous heat-conducting Newtonian fluid in a long and narrow rectangular basin is studied. The heat-physical characteristics depend substantially on the temperature, which, in turn, is a function of coordinates and time. The problem on a flow optimal control with a quadratic quality functional is considered. The heat flow to a free surface of a fluid is assumed to be a control parameter. By the maximum principle of Pontryagin some conditions of a control optimality are found. The problem considered has arosen from studying one of the glass melting problems.