Control problems governed by a pseudo-parabolic partial differential equation

Author:
Luther W. White

Journal:
Trans. Amer. Math. Soc. **250** (1979), 235-246

MSC:
Primary 49B22; Secondary 49A22

DOI:
https://doi.org/10.1090/S0002-9947-1979-0530053-5

MathSciNet review:
530053

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *G* be a bounded domain in and . We consider the solution of the pseudo-parabolic initial-value problem

, to be the state corresponding to the control

*u*. Here and are symmetric uniformly strongly elliptic second-order partial differential operators. The control problem is to find a control in a fixed ball in such that (i) the endpoint of the corresponding state lies in a given neighborhood of a target

*Z*in and (ii) minimizes a certain energy functional. In this paper we establish results concerning the controllability of the states and the compatibility of the constraints, existence and uniqueness of the optimal control, existence and properties of Lagrange multipliers associated with the constraints, and regularity properties of the optimal control.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0530053-5

Keywords:
Pseudo-parabolic equation,
optimal control,
Lagrange multiplier,
controllability,
Lagrangian,
regularity,
target set

Article copyright:
© Copyright 1979
American Mathematical Society