On the Chernous’ko time-optimal problem for the equation of heat conductivity in a rod. (English) Zbl 1448.49027

Summary: The time-optimal problem for the controllable equation of heat conductivity in a rod is considered. By means of the Fourier expansion, the problem reduced to a countable system of one-dimensional control systems with a combined constraint joining control parameters in one relation. In order to improve the time of a suboptimal control constructed by F. L. Chernous’ko, a method of grouping coupled terms of the Fourier expansion of a control function is applied, and a synthesis of the improved suboptimal control is obtained in an explicit form.


49K20 Optimality conditions for problems involving partial differential equations
35K05 Heat equation
74F05 Thermal effects in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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