On the Time-Optimal Control Problem Associated with the Heating Process of a Thin Rod
Farrukh Dekhkonov, E. I. Kuchkorov
Abstract
Abstract In this paper, a boundary control problem for a parabolic equation on the interval is considered. In the part of the bound of the given region value of the solution is given and control, which gives us the average value of solution, is founded. By the method of mathematical physics is proved that control exists and the estimate of a minimal time for achieving the given average temperature over some domain is founded.
Topics & Concepts
MathematicsInterval (graph theory)Control (management)Optimal controlBoundary value problemDomain (mathematical analysis)Process (computing)Value (mathematics)Boundary (topology)Mathematical analysisUpper and lower boundsApplied mathematicsCalculus (dental)Mathematical optimizationCombinatoricsComputer scienceStatisticsMedicineOperating systemArtificial intelligenceDentistryAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential EquationsNumerical methods in inverse problems