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Mathematical control theory of applied partial differential equations is built on linear andnonlinearfunctionalanalysisand manyexistencetheoremsin controlt- ory result from applications of theorems in functional analysis. This makes control theoryinaccessibleto studentswhodo nothave a backgroundin functionalanalysis. Many advanced control theory books on in?nite-dimensionalsystems were wr- ten, using functional analysis and semigroup theory, and control theory was p- sented in an abstract setting. This motivates me to write this text for control theory classes in the way to present control theory by concrete examples and try to m- imize the use of functional analysis. Functional analysis is not assumed and any analysis included here is elementary, using calculus such as integration by parts. The material presented in this text is just a simpli?cation of the material from the existing advanced control books. Thus this text is accessible to senior undergra- ate studentsand?rst-yeargraduatestudentsin appliedmathematics,who havetaken linear algebra and ordinary and partial differential equations. Elementary functional analysis is presented in Chapter 2. This material is - quired to present the control theory of partial differential equations. Since many control conceptsand theories for partial differentialequations are transplanted from ?nite-dimensionalcontrol systems, a brief introduction to feedback control of these systemsispresentedinChapter3.Thetopicscoveredinthischapterincludecontr- lability, observability,stabilizability, pole placement, and quadratic optimal control.

Mathematics. --- Partial Differential Equations. --- Applications of Mathematics. --- Control. --- Differential equations, partial. --- Mathématiques --- Control theory --- Wave equation --- Control theory. --- Feedback control systems. --- Wave equation.

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Although nonlinear waves occur in nearly all branches of physics and engi­ neering, there is an amazing degree of agreement about the fundamental con­ cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin­ istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica­ tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

Engineering. --- Engineering Fluid Dynamics. --- Math. Applications in Geosciences. --- Applications of Mathematics. --- Mathematical Methods in Physics. --- Fluids. --- Continuum Mechanics and Mechanics of Materials. --- Mathematics. --- Mathematical physics. --- Materials. --- Hydraulic engineering. --- Ingénierie --- Mathématiques --- Physique mathématique --- Fluides --- Matériaux --- Technologie hydraulique --- Fluid dynamics. --- Nonlinear wave equations. --- Nonlinear waves. --- Wave-motion, Theory of. --- Nonlinear waves --- Fluid dynamics --- Wave-motion, Theory of --- Nonlinear wave equations --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Applied Mathematics --- Civil Engineering --- Undulatory theory --- Earth sciences. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Continuum mechanics. --- Fluid mechanics. --- Earth Sciences, general. --- Fluid- and Aerodynamics. --- Mechanics --- Wave equation --- Dynamics --- Fluid mechanics --- Nonlinear theories --- Waves --- Geography. --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Engineering, Hydraulic --- Engineering --- Hydraulics --- Shore protection --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Quantum theory --- Physical mathematics --- Math --- Science --- Cosmography --- Earth sciences --- World history --- Mathematics --- Hydrostatics --- Permeability --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Engineering analysis --- Mathematical analysis --- Geosciences --- Environmental sciences --- Hydromechanics --- Continuum mechanics

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The dissipative soliton concept is a fundamental extension of the concept of solitons in conservative and integrable systems. It includes ideas from three major sources, namely standard soliton theory developed since the 1960s, nonlinear dynamics theory, and Prigogine's ideas of systems far from equilibrium. These three sources also correspond to the three component parts of this novel paradigm. This book explains the above principles in detail and gives the reader various examples from optics, biology and medicine. These include laser systems, optical transmission lines, cortical networks, models of muscle contraction, localized vegetation structures and waves in brain tissues.

Solitons --- Energy dissipation --- Dissipation d'énergie --- Quantum Theory --- Biology --- Optics and Photonics --- Nuclear Physics --- Physics --- Engineering --- Biological Science Disciplines --- Natural Science Disciplines --- Technology, Industry, and Agriculture --- Disciplines and Occupations --- Technology, Industry, Agriculture --- Atomic Physics --- Physical Sciences & Mathematics --- Solitons. --- Energy dissipation. --- Dissipation d'énergie --- EPUB-LIV-FT LIVPHYSI SPRINGER-B --- Degradation, Energy --- Dissipation (Physics) --- Energy degradation --- Energy losses --- Losses, Energy --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Physics. --- Neurobiology. --- Applied mathematics. --- Engineering mathematics. --- Quantum optics. --- Lasers. --- Photonics. --- Laser Technology, Photonics. --- Quantum Optics. --- Applications of Mathematics. --- Force and energy --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Mathematics. --- Optics, Lasers, Photonics, Optical Devices. --- Math --- Science --- Neurosciences --- Engineering analysis --- Mathematical analysis --- Optics --- Photons --- Quantum theory --- New optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Mathematics

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Analytical and Hybrid Methods in the Theory of Slot-hole Coupling of Electrodynamic Volumes arose from the original research results, never before published, first obtained by the authors at Karazin Kharkov National University, Ukraine. Impetuous development of technical opportunities of PC for the last twenty years, and a powerful set of numerical methods available in the arsenals of investigators have forced the working-outs connected with the search of analytical solutions of radiophysical problems backward. However, at present, the fact is evident that optimal use of computer calculations should be based on application of analytical methods of boundary problems solution. These methods allow to increase PC use efficiency and also expand their calculation abilities to solve complex electrodynamic problems. The authors’ experience in the development of analytical methods to solve the problems of diffraction of waveguide electromagnetic waves on slot coupling holes serves as a useful tool to readers interested in both the field of theoretical electrodynamics and the field of practical workings-out of multi-functional waveguide devices and systems using slot-coupling elements. Topics covered in this book are: problem formulation and initial integral equations the averaging method analytical solution of the integral equations for a current induced magnetomotive forces method for analysis of coupling slots in waveguides resonant iris with the slot arbitrary oriented in a rectangular waveguide stepped junction of the two rectangular waveguides with the impedance slotted iris This book is intended for academic and industrial researchers involved in Microwave Techniques, as well as advanced students studying Radiophysics and Applied Electrodynamics.

Engineering. --- Microwaves, RF and Optical Engineering. --- Engineering, general. --- Electromagnetism, Optics and Lasers. --- Electromagnetism. --- Microwaves. --- Ingénierie --- Electromagnétisme --- Micro-ondes --- Electrodynamics. --- Physics. --- Relativity (Physics). --- Wave guides. --- Electrodynamics --- Wave guides --- Physics --- Physical Sciences & Mathematics --- Electricity & Magnetism --- Waveguides --- Optical engineering. --- Dynamics --- Electric conductors --- Electric waves --- Electromagnetic waves --- Gyrators --- Microwave transmission lines --- Radio --- Transducers --- Equipment and supplies --- Construction --- Industrial arts --- Technology --- Hertzian waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Mechanical engineering

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This book describes several tractable theories for fluid flow in porous media while the important mathematical questions about structural stability and spatial decay are addressed. Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed, and waves in an elastic body with voids are investigated. Acoustic waves in porous media are also analysed in some detail. A chapter is included on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathematical Sciences at Durham University, United Kingdom.

Mathematics. --- Mechanics. --- Engineering Fluid Dynamics. --- Mechanics, Fluids, Thermodynamics. --- Partial Differential Equations. --- Differential equations, partial. --- Thermodynamics. --- Hydraulic engineering. --- Mathématiques --- Thermodynamique --- Mécanique --- Technologie hydraulique --- Porous materials --Permeability --Mathematical models. --- Transport theory --Mathematical models. --- Wave-motion, Theory of. --- Porous materials --- Transport theory --- Wave-motion, Theory of --- Atomic Physics --- Mathematical Theory --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Permeability --- Mathematical models --- Mathematical models. --- Undulatory theory --- Porous media --- Materials science. --- Partial differential equations. --- Continuum physics. --- Fluid mechanics. --- Materials Science. --- Materials Science, general. --- Classical Continuum Physics. --- Hydromechanics --- Continuum mechanics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Classical field theory --- Continuum physics --- Partial differential equations --- Material science --- Physical sciences --- Mechanics --- Materials --- Porosity --- Materials. --- Classical and Continuum Physics. --- Classical Mechanics. --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Engineering materials --- Industrial materials --- Engineering design --- Manufacturing processes