An efficient heat problem

Abstract

. By means of fi xed point theory we study properties of solutions of a Volterra integral heat equation by fi mapping it into where is the resolvent of JA , J is a large positive number, and f is bounded. It turns out that the linear part has a unique fi xed point which is a uniformly good approximation of a fi xed point for the non- linear equation.Theobjective is to obtain conditions under which the heat applied by a ( t ) concentrates on the solution x ( t ) .