Optimization of heat flux in domains with temperature constraints

In this paper, we deal with a heat flux optimization problem. We maximize the heat output flow on a portion of a domain's boundary, while on the other portion the distribution of the temperature is fixed. The maximization is carried out under the condition that there are no phase changes.The problem is solved using a convex-functional optimization technique, on Banach spaces, within restricted sets, yielding existence and uniqueness of the solution. The explicit form of the solution and the corresponding Lagrange multipliers associated to the problem are also given.In addition, other optimization problems related to the maximum bound of the heat flux with no phase change are solved.This investigation has been supported by the research and development projects Numerical Analysis of Variational Equalities and Inequalities and Free Boundary Problems in Mathematical Physics from CONICET-UNR, Rosario, Argentina.