Von Karman Evolution Equations: Well-posedness and Long Time Dynamics (Springer Monographs in Mathematics)

In the study of mathematical models that arise in the context of concrete - plications, the following two questions are of fundamental importance: (i) we- posedness of the model, including existence and uniqueness of solutions; and (ii) qualitative properties of solutions. A positive answer to the ?rst question, - ing of prime interest on purely mathematical grounds, also provides an important test of the viability of the model as a description of a given physical phenomenon. An answer or insight to the second question provides a wealth of information about the model, hence about the process it describes. Of particular interest are questions related to long-time behavior of solutions. Such an evolution property cannot be v- i?ed empirically, thus any in a-priori information about the long-time asymptotics can be used in predicting an ultimate long-time response and dynamical behavior of solutions. In recent years, this set of investigations has attracted a great deal of attention. Consequent efforts have then resulted in the creation and infusion of new methods and new tools that have been responsible for carrying out a successful an- ysis of long-time behavior of several classes of nonlinear PDEs.

Lasiecka, Irena

Chueshov, Igor

Reference

Springer

This is the first volume of a comprehensive and up-to-date treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume I includes the abstract parabolic theory (continuous theory and numerical approximation theory) for the finite and infinite cases and corresponding PDE illustrations, and presents numerous new results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

Control Theory for Partial Differential Equations: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications)

Science & Math

Mathematics

Cambridge University Press

Volume II focuses on the optimal control problem over a finite time interval for hyperbolic dynamical systems. The chapters consider some abstract models, each motivated by a particular canonical hyperbolic dynamics, and present numerous new results.

Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon: Continuous and Approximation ... and its Applications, Series Number 75)

Triggiani, Roberto

<p>This is the first volume of a comprehensive and up-to-date treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. The authors describe both continuous theory and numerical approximation. They use an abstract space, operator theoretic approach, based on semigroups methods and unifying across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume I includes the abstract parabolic theory (continuous theory and numerical approximation theory) for the finite and infinite cases and corresponding PDE illustrations, and presents numerous new results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.</p>

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications, Series Number 74)

Encyclopedias & Subject Guides

<p>This book presents results on well-posedness, regularity and long-time behavior of non-linear dynamic plate (shell) models described by von Karman evolutions. The coverage is comprehensive and elf-contained, and the theory applies to many similar dynamics.</p>

This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where the structure subject to a frictional damping moves within the fluid. The second chapter then offers a multifaceted description, with often surprising results, of the case of the static interface; a case that is argued in the literature to be a good model for small, rapid oscillations of the structure. The third chapter describes flow-structure interaction where the compressible Navier-Stokes equations are replaced by the linearized Euler equation, while the solid is taken as a nonlinear plate, which oscillates in the surrounding gas flow. The final chapter focuses on a the equations of nonlinear acoustics coupled with linear acoustics or elasticity, as they arise in the context of high intensity ultrasound applications.

Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions (Oberwolfach Seminars, 48)

Kaltenbacher, Barbara

Kukavica, Igor

Tuffaha, Amjad

Webster, Justin T.

Birkhauser

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Functional Analytic Methods for Evolution Equations (Lecture Notes in Mathematics, 1855)

Da Prato, Giuseppe

Kunstmann, Peer Christian

Lunardi, Alessandra

Schnaubelt, Roland

Weis, Lutz

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

Books by Lasiecka, Irena

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

Von Karman Evolution Equations: Well-posedness and Long Time Dynamics (Springer Monographs in Mathematics)

Control Theory for Partial Differential Equations: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications)

Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon: Continuous and Approximation ... and its Applications, Series Number 75)

Control Theory for Partial Differential Equations: Volume 1, Abstract Parabolic Systems: Continuous and Approximation Theories (Encyclopedia of Mathematics and its Applications, Series Number 74)

Von Karman Evolution Equations: Well-posedness and Long Time Dynamics (Springer Monographs in Mathematics)

Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions (Oberwolfach Seminars, 48)

Functional Analytic Methods for Evolution Equations (Lecture Notes in Mathematics, 1855)