Multi Dimensional Hyperbolic Partial Differential Equations

Author : Sylvie Benzoni-Gavage,Denis Serre
Publisher : Oxford University Press on Demand
Page : 535 pages
File Size : 41,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780199211234

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Multi-dimensional Hyperbolic Partial Differential Equations by Sylvie Benzoni-Gavage,Denis Serre Pdf

Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Author : Matthew Witten
Publisher : Elsevier
Page : 268 pages
File Size : 47,6 Mb
Release : 2014-05-23
Category : Mathematics
ISBN : 9781483151359

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Hyperbolic Partial Differential Equations by Matthew Witten Pdf

Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic McKendrick equations for age-structured population growth; and logistic models of structured population growth. A number of book reviews are also included. This journal provides an interdisciplinary forum for the presentation of results not included in other particular journals, and thus will be beneficial to those interested in this field of study.

Author : Luigi Ambrosio,Gianluca Crippa,Camillo De Lellis,Felix Otto,Michael Westdickenberg
Publisher : Springer Science & Business Media
Page : 131 pages
File Size : 51,5 Mb
Release : 2008-02-17
Category : Mathematics
ISBN : 9783540767817

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Transport Equations and Multi-D Hyperbolic Conservation Laws by Luigi Ambrosio,Gianluca Crippa,Camillo De Lellis,Felix Otto,Michael Westdickenberg Pdf

The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. The captivating volume contains surveys of recent deep results and provides an overview of further developments and related open problems. Readers should have basic knowledge of PDE and measure theory.

Author : James Glimm,Andrew J. Majda
Publisher : Unknown
Page : 408 pages
File Size : 47,7 Mb
Release : 1991
Category : Differential equations, Hyperbolic
ISBN : STANFORD:36105031240828

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Multidimensional Hyperbolic Problems and Computations by James Glimm,Andrew J. Majda Pdf

Author : Georges Bastin,Jean-Michel Coron
Publisher : Birkhäuser
Page : 307 pages
File Size : 43,5 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319320625

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Stability and Boundary Stabilization of 1-D Hyperbolic Systems by Georges Bastin,Jean-Michel Coron Pdf

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

Author : Sergey I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin
Publisher : Walter de Gruyter
Page : 188 pages
File Size : 47,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783110960716

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Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems by Sergey I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin Pdf

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection method and prove theorems of convergence, conditional stability, and other properties of the mentioned methods.

Author : Peter D. Lax
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 51,5 Mb
Release : 2006
Category : Differential equations, Hyperbolic
ISBN : 9780821835760

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Hyperbolic Partial Differential Equations by Peter D. Lax Pdf

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Author : Irena Lasiecka,Roberto Triggiani
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2014-02-20
Category : Electronic
ISBN : 1299748929

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Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-Like Systems Over a Finite Time Horizon by Irena Lasiecka,Roberto Triggiani Pdf

Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.

Author : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 53,5 Mb
Release : 2010-10-01
Category : Mathematics
ISBN : 9780821849767

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Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations Pdf

This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

Author : Yuxi Zheng
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201410

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Systems of Conservation Laws by Yuxi Zheng Pdf

This work should serve as an introductory text for graduate students and researchers working in the important area of partial differential equations with a focus on problems involving conservation laws. The only requisite for the reader is a knowledge of the elementary theory of partial differential equations. Key features of this work include: * broad range of topics, from the classical treatment to recent results, dealing with solutions to 2D compressible Euler equations * good review of basic concepts (1-D Riemann problems) * concrete solutions presented, with many examples, over 100 illustrations, open problems, and numerical schemes * numerous exercises, comprehensive bibliography and index * appeal to a wide audience of applied mathematicians, graduate students, physicists, and engineers Written in a clear, accessible style, the book emphasizes more recent results that will prepare readers to meet modern challenges in the subject, that is, to carry out theoretical, numerical, and asymptotical analysis.

Author : Li Ta-tsien,Jiang Song
Publisher : World Scientific
Page : 792 pages
File Size : 49,9 Mb
Release : 2012-09-28
Category : Mathematics
ISBN : 9789814417105

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Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes) by Li Ta-tsien,Jiang Song Pdf

This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ';Hyperbolic Partial Differential Equations';. It is aimed at mathematicians, researchers in applied sciences and graduate students.

Author : Shuxing Chen
Publisher : World Scientific
Page : 207 pages
File Size : 51,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814304832

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Analysis of Singularities for Partial Differential Equations by Shuxing Chen Pdf

The book provides a comprehensive overview on the theory on analysis of singularities for partial differential equations (PDEs). It contains a summarization of the formation, development and main results on this topic. Some of the author's discoveries and original contributions are also included, such as the propagation of singularities of solutions to nonlinear equations, singularity index and formation of shocks.

Author : Durdimurod K. Durdiev,Zhanna D. Totieva
Publisher : Springer Nature
Page : 390 pages
File Size : 44,6 Mb
Release : 2023-06-18
Category : Mathematics
ISBN : 9789819922604

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Kernel Determination Problems in Hyperbolic Integro-Differential Equations by Durdimurod K. Durdiev,Zhanna D. Totieva Pdf

This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional “impacts” or “explosions”. This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.

Author : Elena Obolashvili
Publisher : CRC Press
Page : 164 pages
File Size : 52,6 Mb
Release : 1999-01-06
Category : Mathematics
ISBN : 0582317495

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Partial Differential Equations in Clifford Analysis by Elena Obolashvili Pdf

Clifford analysis represents one of the most remarkable fields of modern mathematics. With the recent finding that almost all classical linear partial differential equations of mathematical physics can be set in the context of Clifford analysis-and that they can be obtained without applying any physical laws-it appears that Clifford analysis itself can suggest new equations or new generalizations of classical equations that may have some physical content. Partial Differential Equations in Clifford Analysis considers-in a multidimensional space-elliptic, hyperbolic, and parabolic operators related to Helmholtz, Klein-Gordon, Maxwell, Dirac, and heat equations. The author addresses two kinds of parabolic operators, both related to the second-order parabolic equations whose principal parts are the Laplacian and d'Alembertian: an elliptic-type parabolic operator and a hyperbolic-type parabolic operator. She obtains explicit integral representations of solutions to various boundary and initial value problems and their properties and solves some two-dimensional and non-local problems. Written for the specialist but accessible to non-specialists as well, Partial Differential Equations in Clifford Analysis presents new results, reformulations, refinements, and extensions of familiar material in a manner that allows the reader to feel and touch every formula and problem. Mathematicians and physicists interested in boundary and initial value problems, partial differential equations, and Clifford analysis will find this monograph a refreshing and insightful study that helps fill a void in the literature and in our knowledge.

Author : S. I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin
Publisher : Walter de Gruyter
Page : 196 pages
File Size : 43,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9067644161

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Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems by S. I. Kabanikhin,Abdigany D. Satybaev,Maxim A. Shishlenin Pdf

The authors consider dynamic types of inverse problems in which the additional information is given by the trace of the direct problem on a (usually time-like) surface of the domain. They discuss theoretical and numerical background of the finite-difference scheme inversion, the linearization method, the method of Gel'fand-Levitan-Krein, the boundary control method, and the projection methodand prove theorems of convergence, conditional stability, and other properties of the mentioned methods.