# Optimal Control Of Partial Differential Equations Theory Methods And Applications Pdf

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Published: 24.05.2021  Linear and non-linear partial differential equations PDEs constitute one of the most widely used mathematical framework for modelling various physical or technological processes, such as fluid flow, structural deformations, propagation of acoustic and electromagnetic waves among countless other examples.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines.

## Optimal control of partial differential equations and nonlinear optimization

Correspondence should be addressed to Xinguang Zhang; zxg This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This special issue focuses on the theme Complex Boundary Value Problems of Nonlinear Differential Equations: Theory, Computational Methods, and Applications which plays a tremendous role in the study and control of the real-world systems and the development of new technologies. The special issue aim is to present some of the recent developments in this field. The issue contains 36 papers selected through a peer-reviewed process. ## Control Theory of Systems Governed by Partial Differential Equations

Dedicated to Prof. Eduardo Casas on the occasion of his 60th birthday. In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under suitable conditions. These conditions comprise second-order sufficient optimality conditions as well as regularity conditions on the control, which consists of a source condition and a condition on the active sets. In addition, we show that these conditions are necessary for convergence rates under certain conditions. We also consider sparse optimal control problems and derive regularization error estimates for them. ## Optimal Control of Partial Differential Equations: Theory, Methods and Applications

The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. Optimal control of partial differential equations and nonlinear optimization Mathematical research topic of WIAS.

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