Boundary Control Of Quasi Linear Hyperbolic Initial Boundary Value Problem
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Boundary Control of Quasi-Linear Hyperbolic Initial Boundary-Value Problem
Author: Jonathan de Halleux
language: en
Publisher: Presses univ. de Louvain
Release Date: 2004
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.
Initial-Boundary Value Problems and the Navier-Stokes Equation
Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. 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 book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.
Trends in Partial Differential Equations of Mathematical Physics
Author: José F. Rodrigues
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-03-30
This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.