Regularity and optimal control of quasicoupled and coupled heating processes

Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions of such systems, the technique of spaces of Běsov-Sobolev type is essentially employed and the possibility of its use when solving optimization problems is studied.