On the solvability of the problem of the distributed optimal control of oscillation processes described by the Fredholm integro-differential equations

Subject	Optimization
Title	On the solvability of the problem of the distributed optimal control of oscillation processes described by the Fredholm integro-differential equations
Author(s)	Akylbek Kerimbekov, Elmira Abdyldaeva
Keywords	Functional, boundary value problem, the optimality condition, nonlinear integral equation, optimal control.
Abstract	In this paper we have investigated the problem of tracking, where is required to minimize the functional J[u(t) ]=∫_0^T▒∫_Q▒[V(t,x)-ξ(t,x) ] ^2 dxdt+β∫_0^T▒〖∫_Q▒p^2 [t,x,u(t,x) ]dxdt〗, β>0, on the set of solutions of the boundary value problem V_tt-AV=λ∫_0^T▒K(t,τ)V(τ,x) dτ+f[t,x,u(t,x) ], x∈Q⊂R^n,0

On the solvability of the problem of the optimal control of thermal processes described by the Fredholm integro-differential equations

Subject	Optimization
Title	On the solvability of the problem of the optimal control of thermal processes described by the Fredholm integro-differential equations
Author(s)	Akylbek Kerimbekov, Raikan Nametkulova
Keywords	Functional, boundary value problem, the optimality condition, nonlinear integral equation, optimal control.
Abstract	In this paper we have investigated the problem of tracking, where is required to minimize the functional J[u(t) ]=∫_0^T▒∫_Q▒[V(t,x)-ξ(t,x) ] ^2 dxdt+β∫_0^T▒〖u^2 (t)dt, β>0〗, on the set of solutions of the boundary value problem V_t-AV=λ∫_0^T▒K(t,τ)V(τ,x) dτ+g[t,x]f[t,u(t) ], x∈Q⊂R^n,0

On the solvability of the problem of the optimal control of thermal processes described by the Volterra integro-differential equations

Subject	Optimization
Title	On the solvability of the problem of the optimal control of thermal processes described by the Volterra integro-differential equations
Author(s)	Akylbek Kerimbekov, Bahytjamal Kulbaeva
Keywords	Functional, boundary value problem, the optimality condition, nonlinear integral equation, optimal control.
Abstract	In this paper we have investigated the problem of tracking, where is required to minimize the functional J[u(t) ]=∫_0^T▒∫_Q▒[V(t,x)-ξ(t,x) ] ^2 dxdt+β∫_0^T▒〖|u(t) |dt, β>0〗, on the set of solutions of the boundary value problem V_t-AV=λ∫_0^t▒K(t,τ)V(τ,x) dτ+g[t,x]f[t,u(t) ], x∈Q⊂R^n,0

On the solvability of the problem of the optimal boundary control of thermal processes described by the Fredholm integro-differential equations

Subject	Optimization
Title	On the solvability of the problem of the optimal boundary control of thermal processes described by the Fredholm integro-differential equations
Author(s)	Akylbek Kerimbekov, Aisha Kadirimbetova
Keywords	Functional, boundary value problem, the optimality condition, nonlinear integral equation, optimal control.
Abstract	In this paper we have investigated the problem of tracking, where is required to minimize the functional J[u(t) ]=∫_0^T▒∫_Q▒[V(t,x)-ξ(t,x) ] ^2 dxdt+β∫_0^T▒〖u^2 (t)dt, β>0〗, on the set of solutions of the boundary value problem V_t-AV=λ∫_0^T▒K(t,τ)V(τ,x) dτ+g[t,x], x∈Q⊂R^n, 0