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Author :
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (778 download)
Download or read book Distributed Optimal Control of a Nonstandard System of Phase Field Equations written by and published by . This book was released on 2011 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (962 download)
Download or read book Distributed Optimal Control of a Nonstandard Nonlocal Phase Field System written by Pierluigi Colli and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (962 download)
Download or read book Distributed Optimal Control of a Nonstandard Nonlocal Phase Field System with Double Obstacle Potential written by Pierluigi Colli and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with a distributed optimal control problem for a nonlocal phase field model of Cahn-Hilliard type, which is a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion. The local model has been investigated in a series of papers by P. Podio-Guidugli and the present authors the nonlocal model studied here consists of a highly nonlinear parabolic equation coupled to an ordinary differential inclusion of subdifferential type. The inclusion originates from a free energy containing the indicator function of the interval in which the order parameter of the phase segregation attains its values. It also contains a nonlocal term modeling long-range interactions. Due to the strong nonlinear couplings between the state variables (which even involve products with time derivatives), the analysis of the state system is difficult. In addition, the presence of the differential inclusion is the reason that standard arguments of optimal control theory cannot be applied to guarantee the existence of Lagrange multipliers. In this paper, we employ recent results proved for smooth logarithmic potentials and perform a so-called 'deep quench' approximation to establish existence and first-order necessary optimality conditions for the nonsmooth case of the double obstacle potential.
Author : Pierluigi Colli
Publisher : Springer
ISBN 13 : 3319644890
Total Pages : 572 pages
Book Rating : 4.3/5 (196 download)
Download or read book Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs written by Pierluigi Colli and published by Springer. This book was released on 2017-11-03 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (83 download)
Download or read book Analysis and optimal boundary control of a nonstandard system of phase field equations written by Pierluigi Colli and published by . This book was released on 2012 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Hintermüller
Publisher : Springer Nature
ISBN 13 : 3030331164
Total Pages : 396 pages
Book Rating : 4.0/5 (33 download)
Download or read book Topics in Applied Analysis and Optimisation written by Michael Hintermüller and published by Springer Nature. This book was released on 2019-11-27 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
Author : Dan Tiba
Publisher : Springer
ISBN 13 : 3540467556
Total Pages : 166 pages
Book Rating : 4.5/5 (44 download)
Download or read book Optimal Control of Nonsmooth Distributed Parameter Systems written by Dan Tiba and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.
Author : Alfred C. Robinson
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.3/5 (91 download)
Download or read book A Survey of Optimal Control of Distributed-parameter Systems written by Alfred C. Robinson and published by . This book was released on 1969 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report is a survey of theoretical and computational methods in the field of optimal control of distributed parameter systems. This includes systems described by integral equations and partial differential equations. The various studies which have been done are grouped according to the method employed. A number of applications and potential applications of these methods are discussed, and certain deficiencies in the current state of knowledge are noted. Difficulties and opportunities in practical applications are discussed, and suggestions are offered for directions of research to render the results more readily usable. A list of references is included numbering more than 250 items: papers, report, and books.
Author : Costica Morosanu
Publisher : Bentham Science Publishers
ISBN 13 : 1608053504
Total Pages : 353 pages
Book Rating : 4.6/5 (8 download)
Download or read book Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods written by Costica Morosanu and published by Bentham Science Publishers. This book was released on 2011-04-27 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: "All developments in mathematics and computer science facilitate development of industrial applications. This e-book approaches the subject in a profoundly interdisciplinary manner.The spectrum of subjects covered in this e-book includes mathematics, comp"
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (93 download)
Download or read book Regulatity of the Solution to a Nonstandard System of Phase Field Equations written by Pierluigi Colli and published by . This book was released on 2013 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. L. Lions
Publisher : SIAM
ISBN 13 : 9781611970616
Total Pages : 98 pages
Book Rating : 4.9/5 (76 download)
Download or read book Some Aspects of the Optimal Control of Distributed Parameter Systems written by J. L. Lions and published by SIAM. This book was released on 1972-01-01 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The applications of the theory of Optimal Control of distributed parameters is an extremely wide field and, although a large number of questions remain open, the whole subject continues to expand very rapidly. The author does not attempt to cover the field but does discuss a number of the more interesting areas of application.
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (93 download)
Download or read book Regulatity of the Solution to a Nonstandard System of Phase Field Equations written by Pierluigi Colli and published by . This book was released on 2013 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (93 download)
Download or read book A continuous dependence result for a nonstandard system of phase field equations written by Pierluigi Colli and published by . This book was released on 2013 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Qi Lü
Publisher : Springer Nature
ISBN 13 : 3030823318
Total Pages : 592 pages
Book Rating : 4.0/5 (38 download)
Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü and published by Springer Nature. This book was released on 2021-10-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.
Author : Jacques-Louis Lions
Publisher : Bordas Editions
ISBN 13 :
Total Pages : 586 pages
Book Rating : 4.:/5 (44 download)
Download or read book Control of Distributed Singular Systems written by Jacques-Louis Lions and published by Bordas Editions. This book was released on 1985 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: " ... the purpose of this book is to describe and analyse (and to some extent generalise) the principal results, scattered in the literature, concerning perturbation methods in optimal control for systems that are governed by deterministic or stochastic differential equations."--Preface.
Author : Shlomo Ta'asan
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (317 download)
Download or read book "One Shot" Methods for Optimal Control of Distributed Parameter Systems I: Finite Dimensional Control written by Shlomo Ta'asan and published by . This book was released on 1991 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierluigi Colli
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (94 download)
Download or read book A vanishing diffusion limit in a nonstandard system of phase field equations written by Pierluigi Colli and published by . This book was released on 2012 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
