<p>This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia~i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems.</p>

Mathematical Methods in Optimization of Differential Systems (Mathematics and Its Applications, 310)

Barbu, Viorel

Reference

Springer

Stabilization of Navier–Stokes Flows (Communications and Control Engineering)

<p>Stabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still. Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular.</p>

<p>This volume presents recent and notable progress in the mathematical theory of stabilization of Newtonian fluid flows. It avoids the tedious technical details often seen in mathematical treatments of the subject and will thus appeal to a wide range of readers.</p>

<p><div>This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier-Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise.&nbsp;</div> <div><br /></div> <div>Intended for graduate students and researchers working on control problems involving nonlinear differential equations, <i>Controllability and Stabilization of Parabolic Equations</i> is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.&nbsp;&nbsp;</div> <div><br /></div></p>

Controllability and Stabilization of Parabolic Equations (PNLDE Subseries in Control)

Birkhauser

<p><p>This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions.</p> <p>The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory.</p></p>

Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts (Lecture Notes in Mathematics, 2353)

Science & Math

Röckner, Michael

Mathematics

<p>Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found.<br>The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".<br>The book will be of interest to PhD students and researchers in mathematics, physics and biology.</p>

Stochastic Porous Media Equations (Lecture Notes in Mathematics, 2163)

Da Prato, Giuseppe

<p>This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner.<br>Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, <i>Differential Equations</i> is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations.<br>Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.<br></p>

Differential Equations (Springer Undergraduate Mathematics Series)

<p>This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. <br>Intended for graduate students and researchers working on control problems involving nonlinear differential equations, <i>Controllability and Stabilization of Parabolic Equations</i> is the distillation of years of lectures and research. With a minimum of preliminaries, the book leaps into its applications for control theory with both concrete examples and accessible solutions to problems in stabilization and controllability that are still areas of current research.  <br></p>

Controllability and Stabilization of Parabolic Equations (Progress in Nonlinear Differential Equations and Their Applications, 90)

<p>This book is concerned with nonlinear semigroups of contractions in Banach spaces and their application to the existence theory for differential equa tions associated with nonlinear dissipative operators. The study of nonlinear semi groups resulted from the examination of nonlinear parabolic equations and from various nonlinear boundary value problems. The first work done by Y. Komura stimulated much further work and interest in this subject. Thus a series of studies was begun and then continued by T. Kato, M. G. Crandall, A. Pazy, H. Brezis and others, who made important con tributions to the development of the theory. The theory as developed below is a generalisation of the Hille-Yosida theory for one-parameter semigroups of linear operators and is a collection of diversified results unified more or less loosely by their methods of approach. This theory is also closely related to the theory of nonlinear monotone operators. Of course not all aspects of this theory could be covered in our expo sition, and many important contributions to the subject have been excluded for the sake of brevity. We have attempted to present the basic results to the reader and to orient him toward some of the applications. This book is intended to be self-contained. The reader is assumed to have only a basic knowledge of functional analysis, function theory and partial differential equations. Some of the necessary prerequisites for the reading of this 'book are summarized, with or without proof, in Chapter I.</p>

Nonlinear semigroups and differential equations in Banach spaces

<p>This volume is concerned with a few basic results in the classical and modern theory of boundary value problems for elliptic, parabolic and wave equations. The emphasis is on understanding the main results of the field, along with a few classical and modern methods. Weak solutions to boundary value problems of parabolic and hyperbolic type are also included. Furthermore, topics such as the maximum principle and potentials are presented. Audience: The book can be recommended for a graduate level course, and will be of interest to researchers and graduate students whose work involves partial differential equations, mathematics of physics and of engineering, potential theory and calculus of variations.</p>

Partial Differential Equations and Boundary Value Problems (Mathematics and Its Applications)

See the best price to sell, buy, or rent books by Barbu, Viorel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Barbu, Viorel

See the best price to sell, buy, or rent books by Barbu, Viorel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Mathematical Methods in Optimization of Differential Systems (Mathematics and Its Applications, 310)

Stabilization of Navier–Stokes Flows (Communications and Control Engineering)

Stabilization of Navier–Stokes Flows (Communications and Control Engineering)

Controllability and Stabilization of Parabolic Equations (PNLDE Subseries in Control)

Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts (Lecture Notes in Mathematics, 2353)

Stochastic Porous Media Equations (Lecture Notes in Mathematics, 2163)

Differential Equations (Springer Undergraduate Mathematics Series)

Controllability and Stabilization of Parabolic Equations (Progress in Nonlinear Differential Equations and Their Applications, 90)

Nonlinear semigroups and differential equations in Banach spaces

Partial Differential Equations and Boundary Value Problems (Mathematics and Its Applications)