The Classical Continuous Optimal Control for Quaternary Nonlinear Parabolic Boundary Value Problems

An optimal analytical method for nonlinear boundary value problems based on method of variation of parameter

In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate soluti...

Optimal Control Problems for Parabolic Hemivariational Inequalities with Boundary Conditions

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control fo...

Continuous Dependence on Data for Quasiautonomous Nonlinear Boundary Value Problems

Here A : D(A) ⊆H →H is a maximal monotone operator (possibly multivalued) in a real Hilbert space H , D(A) is its domain, a,b ∈ D(A), f ∈ L2(0,T ;H), and p, r are two continuous functions from [0,T] to R. In [10, 11], Barbu proved the existence of the solution in the case p ≡ 1, r ≡ 0. The author considered the boundary value problems u′′(t) ∈Au(t) + f (t), a.e. t ∈ (0,T), u(0) = a, u(T) = b, (...

Initial - Boundary Value Problems for Parabolic Equations

Optimal boundary control problems of retarded parabolic systems

Various optimal control problems of infinite dimensional systems with point and distributed delays were considered in [1], [2], [3], [5], [6], [7], [8], [9], [10] and [15]. In [15], optimal control problems for parabolic systems with Neumann boundary conditions involving constant time delays were considered. Such systems constitute in a linear approximation, a universal mathematical model for m...