Solvability Regularity And Optimal Control Of Boundary Value Problems For Pdes
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Solvability Regularity And Optimal Control Of Boundary Value Problems For Pdes
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Author : Pierluigi Colli
language : en
Publisher: Springer
Release Date : 2017-11-03
Solvability Regularity And Optimal Control Of Boundary Value Problems For Pdes written by Pierluigi Colli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-03 with Mathematics categories.
This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Solvability Of Nonlinear Singular Problems For Ordinary Differential Equations
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Author : Irena Rachunkova
language : en
Publisher: Hindawi Publishing Corporation
Release Date : 2009
Solvability Of Nonlinear Singular Problems For Ordinary Differential Equations written by Irena Rachunkova and has been published by Hindawi Publishing Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Boundary value problems categories.
Frontiers In Pde Constrained Optimization
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Author : Harbir Antil
language : en
Publisher: Springer
Release Date : 2018-10-12
Frontiers In Pde Constrained Optimization written by Harbir Antil and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-12 with Mathematics categories.
This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs). As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.
Topics In Applied Analysis And Optimisation
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Author : Michael Hintermüller
language : en
Publisher: Springer Nature
Release Date : 2019-11-27
Topics In Applied Analysis And Optimisation written by Michael Hintermüller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-27 with Mathematics categories.
This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
State Dependent Impulses
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Author : Irena Rachůnková
language : en
Publisher: Springer
Release Date : 2015-09-29
State Dependent Impulses written by Irena Rachůnková and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.
Boundary Stabilization Of Parabolic Equations
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Author : Ionuţ Munteanu
language : en
Publisher: Springer
Release Date : 2019-02-15
Boundary Stabilization Of Parabolic Equations written by Ionuţ Munteanu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-15 with Science categories.
This monograph presents a technique, developed by the author, to design asymptotically exponentially stabilizing finite-dimensional boundary proportional-type feedback controllers for nonlinear parabolic-type equations. The potential control applications of this technique are wide ranging in many research areas, such as Newtonian fluid flows modeled by the Navier-Stokes equations; electrically conducted fluid flows; phase separation modeled by the Cahn-Hilliard equations; and deterministic or stochastic semi-linear heat equations arising in biology, chemistry, and population dynamics modeling. The text provides answers to the following problems, which are of great practical importance: Designing the feedback law using a minimal set of eigenfunctions of the linear operator obtained from the linearized equation around the target state Designing observers for the considered control systems Constructing time-discrete controllers requiring only partial knowledge of the state After reviewing standard notations and results in functional analysis, linear algebra, probability theory and PDEs, the author describes his novel stabilization algorithm. He then demonstrates how this abstract model can be applied to stabilization problems involving magnetohydrodynamic equations, stochastic PDEs, nonsteady-states, and more. Boundary Stabilization of Parabolic Equations will be of particular interest to researchers in control theory and engineers whose work involves systems control. Familiarity with linear algebra, operator theory, functional analysis, partial differential equations, and stochastic partial differential equations is required.
Free Boundary Problems
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Author : A. Bossavit
language : en
Publisher:
Release Date : 1985
Free Boundary Problems written by A. Bossavit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Generalized Characteristics Of First Order Pdes
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Author : Arik Melikyan
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Generalized Characteristics Of First Order Pdes written by Arik Melikyan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs. A well-known classical result states a sufficiency condition for local existence and uniqueness of twice differentiable solution. This result is based on the method of characteristics (MC). Very often, and as a rule in control theory, the continuous nonsmooth (non-differentiable) functions have to be treated as a solutions to the PDE. At the points of smoothness such solutions satisfy the equation in classical sense. But if a function satisfies this condition only, with no requirements at the points of nonsmoothness, the PDE may have nonunique solutions. The uniqueness takes place if an appropriate matching principle for smooth solution branches defined in neighboring domains is applied or, in other words, the notion of generalized solution is considered. In each field an appropriate matching principle are used. In Optimal Control and Differential Games this principle is the optimality of the cost function. In physics and mechanics certain laws must be fulfilled for correct matching. A purely mathematical approach also can be used, when the generalized solution is introduced to obtain the existence and uniqueness of the solution, without being aimed to describe (to model) some particular physical phenomenon. Some formulations of the generalized solution may meet the modelling of a given phenomenon, the others may not.
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems
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Author : Martin Gugat
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems written by Martin Gugat and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Science categories.
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.
Elliptic Boundary Value Problems In Domains With Point Singularities
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Author : V. A. Kozlov
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Elliptic Boundary Value Problems In Domains With Point Singularities written by V. A. Kozlov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Boundary value problems categories.
For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR