The maximum principle in the case of boundary control problems involving the onedimensional heat conduction equation
Abstract
An investigation is conducted of boundary control problems for a plate, a sphere, and a cylinder. A maximum principle formulated by von Wolfersdorf (1975) is considered. The maximum principle had been derived for processes which are described by a system of general integral equations of the Hammerstein type. The problems investigated are reduced to control problems described by a system of Hammerstein integral equations and the maximum principle for these Hammerstein equations is used to derive maximum principles for the control problems involving the heat conduction equations. Nonlinear heating processes are studied.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 January 1976
 DOI:
 10.1002/zamm.19760560105
 Bibcode:
 1976ZaMM...56...25U
 Keywords:

 Boundary Layer Control;
 Conductive Heat Transfer;
 Maximum Principle;
 One Dimensional Flow;
 Thermal Boundary Layer;
 Boundary Value Problems;
 Heat Transmission;
 Integral Equations;
 Nonlinear Equations;
 Specimen Geometry;
 Surface Temperature;
 Temperature Control;
 Temperature Distribution;
 Thermodynamics;
 Fluid Mechanics and Heat Transfer