Download or read book Boundary Control of Quasi Linear Hyperbolic Initial Boundary Value Problem written by Jonathan de Halleux and published by Presses univ. de Louvain. This book was released on 2004 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis presents different control design approaches for stabilizing networks of quasi-linear hyperbolic partial differential equations. These equations are usually conservative, which gives them interesting properties to design stabilizing control laws. Two main design approaches are developed: a methodology based on entropies and Lyapunov functions and a methodology based on the Riemann invariants. The stability theorems are illustrated using numerical simulations. Two practical applications of these methodologies are presented. Network of navigation channels are modelled using the Saint-Venant equation (also known as the Shallow Water Equations). The stabilization problem of such system has an industrial importance in order to satisfy the navigation constraints and to optimize the production of electricity in hydroelectric plants, usually located at each hydraulic gate. A second application deals with the regulation of water waves in moving tanks. This problem is also modelled by a modified version of the shallow water equations and appears in a number industrial fields which deal with liquid moving parts.
Download or read book Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems written by Tatsien Li and published by Springer. This book was released on 2016-11-08 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyperbolic systems.
Download or read book Boundary Value Problems for Quasilinear Hyperbolic Systems written by Daqian Li and published by . This book was released on 1985 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems written by Martin Gugat and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Download or read book Hyperbolic Boundary Value Problems written by Reiko Sakamoto and published by CUP Archive. This book was released on 1982-07-08 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems are of central importance and interest not only to mathematicians but also to physicists and engineers who need to solve differential equations which govern the behaviour of physical systems. In this book, Professor Sakamoto introduces the general theory of the existence and uniqueness of solutions to the wave equation. The reader is assumed to have some familiarity with Lebesgue integration and complex function theory but other than that the book is essentially self-contained. It is therefore suited to senior undergraduates and graduates in mathematics and the mathematical sciences but can be read with profit by professionals in those subjects.
Download or read book Boundary Value Problems and Free Boundary Problems for Quasilinear Hyperbolic Parabolic Coupled Systems written by Ta-tsien Li and published by . This book was released on 1981 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many applications one meets systems of differential equations which consist of first-order hyperbolic and second-order parabolic subsystems which are nonlinearly coupled. These arise, for instance, in the modeling of motion of a compressible, viscous heat conducting fluid, in radiation hydrodynamics, and in the theory of motion of viscoelastic materials. The relevant equations are presented. The results of this work are local time existence and uniqueness theorems for initial-boundary value problems, including cases with free boundaries, for such systems. The results given are for the case of one space dimension. The methods used involve introducing appropriate variables, the method of iteration, a priori estimation and fixed point theorems.
Download or read book Initial boundary value Problems for Quasilinear Symmetric Hyperbolic Systems Existence of Solutions to the Compressible Euler Equations and Their Incompressible Limit written by Steven Schochet and published by . This book was released on 1984 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems for Hyperbolic Partial Differential Equations with Constant Coefficients written by J. F. Heyda and published by . This book was released on 1959 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Initial boundary Value Problems and the Navier Stokes Equations written by Heinz-Otto Kreiss and published by SIAM. This book was released on 1989-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Download or read book Boundary value Problems with Free Boundaries for Elliptic Systems of Equations written by Valentin Nikolaevich Monakhov and published by American Mathematical Soc.. This book was released on 1983 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
Download or read book Boundary Value Problems From Higher Order Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1986-07-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems
Download or read book A free boundary value problem for a quasilinear hyperbolic system written by Hans-Dieter Alber and published by . This book was released on 1988 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Initial Boundary Value Problems for Hyperbolic Systems of Conservation Laws written by Jonathan Bernard Goodman and published by . This book was released on 1982 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Boundary Controllability of Nonlinear Hyperbolic Systems written by Marco Cirina and published by . This book was released on 1968 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Initial boundary Value Problem in Nonlinear Hyperbolic Thermoelasticity written by Jerzy August Gawinecki and published by . This book was released on 2002 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Initial boundary Value Problems for Linear Hyperbolic Partial Differential Equations of the Second Order written by Calvin Hayden Wilcox and published by . This book was released on 1962 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and self-contained treatment of the initial-boundary value problem for a class of linear hyperbolic partial differential equations of the second order is presented. Many conceps and techniques are incorporated and extended. The most basic of the new results is the domain of dependence inequality, which is the keystone of the theory. (Author).
Download or read book Some Problems on Nonlinear Hyperbolic Equations and Applications written by Yuejun Peng and published by World Scientific. This book was released on 2010 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.
