Dual extremum principles for the heat equation
Abstract
Dual extremum principles characterising the solution of initial value problems for the heat equation are obtained by imbedding the problem in twopoint boundaryvalue problem for a system in which the original equation is coupled with its adjoint. Bounds on quantities of interest in the original initialvalue problem are obtained. Such principles are examples of ones which can be obtained for a general class of linear operators on a Hilbert space.
 Publication:

Proceedings of the Royal Society of Edinburgh
 Pub Date:
 1977
 Bibcode:
 1977RSEPS..77..273C
 Keywords:

 Boundary Value Problems;
 Extremum Values;
 Thermodynamics;
 Functionals;
 Hilbert Space;
 Linear Operators;
 Operators (Mathematics);
 Fluid Mechanics and Heat Transfer