Hamilton-Jacobi Equations in Hilbert Spaces

Hamilton-Jacobi Equations in Hilbert Spaces

Author: Viorel Barbu

Publisher: Pitman Advanced Publishing Program

Published: 1983

Total Pages: 188

ISBN-13:

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This presents a self-contained treatment of Hamilton-Jacobi equations in Hilbert spaces. Most of the results presented have been obtained by the authors. The treatment is novel in that it is concerned with infinite dimensional Hamilton-Jacobi equations; it therefore does not overlap with Research Note #69. Indeed, these books are in a sense complementary.


Second Order Partial Differential Equations in Hilbert Spaces

Second Order Partial Differential Equations in Hilbert Spaces

Author: Giuseppe Da Prato

Publisher: Cambridge University Press

Published: 2002-07-25

Total Pages: 206

ISBN-13: 9780521777292

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Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.


Second Order Partial Differential Equations in Hilbert Spaces

Second Order Partial Differential Equations in Hilbert Spaces

Author: Giuseppe Da Prato

Publisher: Cambridge University Press

Published: 2002-07-25

Total Pages: 397

ISBN-13: 1139433431

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State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.


Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations

Author: Martino Bardi

Publisher: Springer Science & Business Media

Published: 2009-05-21

Total Pages: 588

ISBN-13: 0817647554

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This softcover book is a self-contained account of the theory of viscosity solutions for first-order partial differential equations of Hamilton–Jacobi type and its interplay with Bellman’s dynamic programming approach to optimal control and differential games. It will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. The work may be used by graduate students and researchers in control theory both as an introductory textbook and as an up-to-date reference book.


Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control

Author: Piermarco Cannarsa

Publisher: Springer Science & Business Media

Published: 2007-12-31

Total Pages: 311

ISBN-13: 081764413X

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* A comprehensive and systematic exposition of the properties of semiconcave functions and their various applications, particularly to optimal control problems, by leading experts in the field * A central role in the present work is reserved for the study of singularities * Graduate students and researchers in optimal control, the calculus of variations, and PDEs will find this book useful as a reference work on modern dynamic programming for nonlinear control systems


Mathematical Topics in Fluid Mechanics

Mathematical Topics in Fluid Mechanics

Author: Jose Francisco Rodrigues

Publisher: CRC Press

Published: 2020-09-30

Total Pages: 282

ISBN-13: 1000158039

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This Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.


Propagation of a Curved Shock and Nonlinear Ray Theory

Propagation of a Curved Shock and Nonlinear Ray Theory

Author: Prasad

Publisher: CRC Press

Published: 1993-09-27

Total Pages: 140

ISBN-13: 9780582072534

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Phoolan Prasad's book contains theoretical developments in the study of the propagation of a curved nonlinear wave front and shock front, particularly in the caustic region. It should be an invaluable reference source for researchers in nonlinear waves; fluid dynamics (especially gas dynamics); mathematical physics; aeronautical, chemical and mechanical engineering.


Nonstandard Methods in the Calculus of Variations

Nonstandard Methods in the Calculus of Variations

Author: Curtis Tuckey

Publisher: CRC Press

Published: 1993-11-22

Total Pages: 116

ISBN-13: 9780582231801

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This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.


Non-Classical Elastic Solids

Non-Classical Elastic Solids

Author: Michele Ciarletta

Publisher: CRC Press

Published: 2020-11-25

Total Pages: 359

ISBN-13: 1000115267

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Problems concerning non-classical elastic solids continue to attract the attention of mathematicians, scientists and engineers. Research in this area addresses problems concerning many substances, such as crystals, polymers, composites, ceramics and blood. This comprehensive, accessible work brings together recent research in this field, and will be of great interest to mathematicians, physicists and other specialists working in this area.


Cont Markov Chains

Cont Markov Chains

Author: Borkar

Publisher: CRC Press

Published: 1991-04-30

Total Pages: 196

ISBN-13: 9780582068216

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Provides a novel treatment of many problems in controlled Markov chains based on occupation measures and convex analysis. Includes a rederivation of many classical results, a general treatment of the ergodic control problems and an extensive study of the asymptotic behavior of the self-tuning adaptive controller and its variant, the Kumar-Becker-Lin scheme. Also includes a novel treatment of some multiobjective control problems, inaccessible to traditional methods. Annotation copyrighted by Book News, Inc., Portland, OR