Quasi Steady-state Microwave Heating Systems For The Optimal Control Problem

This thesis studies the existence of optimal control problem of quasi-stationary microwave heating system.The controlled system may describe by the following Maxwell equation and the heat conductivity equation coupling:With inicial and boundary value conditions:H = (H₁,H₂,H₃) is the magnetic fields,σ(x,t) and k (x)σ(x,t)separately expressed leads the coefficient and the thermal conductivity for the fax. N|â†'is (?)ΩOutside unit law vector. G(x,t) and g(x,t) is for the boundarycondition which assigns, H₀(x),u₀(x) is the initial condition , q(t) expresses the control. The admit control set is:The cost functional is:Whereδ> 0 is a given constant, u_T(x) is known desired terminal temperature, and u_T∈L²(Ω). Optimal control question (P): find a q₀∈Q , such that, J(q₀)≤J(q), (?)q∈QSubject to (1.1) and (1.2).Therefore, we first under the suitable supposition condition, using the energy estimated the law had proven as follows draws up the stablestate Maxwell equation weak solution the existence: Then, we proved the existence solution of the following quasi-linear parabolic differential equation'by using monotone operator theory:Finally the existence of the optimal control problem.This optimal control aske the exercise key existence certificate may for draw up the stable state microwave heating system optimal control question the further research to provide the rationale.