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On the optimal control problem for the k-FORQ/MCH equation with viscosity

Zhao Wang, Shan Zhang

Abstract

In this paper, we investigate the optimal control problem for the k-FORQ/MCH equation with strong viscosity.We prove the existence and uniqueness of this equation under the initial and boundary conditions by Galerkin method. From these results and the Lion's theory we deduce the existence of an optimal solution to the control problem governed by the viscous k-FORQ/MCH equation. Using augmented Lagrangian method, we deduce the first-order necessary optimality condition and two second-order sufficient optimality conditions.

On the optimal control problem for the k-FORQ/MCH equation with viscosity

Abstract

In this paper, we investigate the optimal control problem for the k-FORQ/MCH equation with strong viscosity.We prove the existence and uniqueness of this equation under the initial and boundary conditions by Galerkin method. From these results and the Lion's theory we deduce the existence of an optimal solution to the control problem governed by the viscous k-FORQ/MCH equation. Using augmented Lagrangian method, we deduce the first-order necessary optimality condition and two second-order sufficient optimality conditions.
Paper Structure (8 sections, 125 equations)

This paper contains 8 sections, 125 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Formation of the optimal control problem
  5. Existence and uniqueness of weak solution
  6. Optimal control problem
  7. First-order nececessary optimality condition
  8. Second-order sufficient optimality condition

Theorems & Definitions (7)

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