Last edited by Kekora
Friday, August 7, 2020 | History

6 edition of Theory and application of hyperbolic systems of quasilinear equations found in the catalog.

Theory and application of hyperbolic systems of quasilinear equations

by Hyun-Ku Rhee

  • 12 Want to read
  • 22 Currently reading

Published by Dover Publications in Mineola, N.Y .
Written in English

    Subjects:
  • Differential equations, Hyperbolic.,
  • Quasilinearization.

  • Edition Notes

    StatementHyun-Ku Rhee, Rutherford Aris, Neal R. Amundson.
    SeriesFirst-order partial differential equations ;, v. 2
    ContributionsAris, Rutherford., Amundson, Neal Russell, 1916-
    Classifications
    LC ClassificationsQA374 .R47 2001 vol. 2, QA377 .R47 2001 vol. 2
    The Physical Object
    Paginationxii, 548 p. :
    Number of Pages548
    ID Numbers
    Open LibraryOL3949756M
    ISBN 100486419940
    LC Control Number2001041183

    APPLICATION OF THE SMOOTHING METHOD TO SOME SYSTEMS OF HYPERBOLIC QUASILINEAR EQUATIONS* SOV Moscow (Receded 24 Decem&er ) THE method of smoothing, which is a convenient and universal means of investigating and calculating the discontinuous solutions of hyperbolic equa- tions, is applied to some specific cases, namely, to the system of Author: N.N. Kuznetsov. An explicit second order method of characteristics is given for the numerical solution of initial boundary value problems for quasilinear hyperbolic first order systems of partial differential equations with two independent variables and its application in fluid by: 1.

    () High-gain observers for a class of 2 × 2 quasilinear hyperbolic systems with 2 different velocities. IFAC-PapersOnLine , () On boundary stability of inhomogeneous 2 × 2 1-D hyperbolic systems for the C 1 by: The Method of Characteristics for Quasilinear Equations • Recall a simple fact from the theory of ODE’s: The equation du dt = f(t,u) can be solved (at least for small values of t) for each initial condition u(0) = u0, provided that f is continuous in t and Lipschitz continuous in the variable Size: KB.

    In [26, pages 33{35] there are examples of systems of linear equations which arise from simple electrical networks using Kirchho ’s laws for elec-trical circuits. Solving a system consisting of a single linear equation is easy. However if we are dealing with two or more equations, it File Size: KB. Chapter 1 Introduction Ordinary and partial differential equations occur in many applications. An ordinary differential equation is a special case of a partial differential equa-File Size: 1MB.


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Theory and application of hyperbolic systems of quasilinear equations by Hyun-Ku Rhee Download PDF EPUB FB2

The book begins with a consideration of pairs of quasilinear hyperbolic equations of the first order and goes on to explore multicomponent chromatography, complications of counter-current moving-bed adsorbers, the adiabatic adsorption column, 5/5(1).

Get this from a library. First-Order Partial Differential Equations. Volume 2, Theory and application of hyperbolic systems of quasilinear equations. [Hyun-Ku Rhee; Rutherford Aris; Neal R Amundson] -- Second volume of a highly regarded two-volume set, fully usable on its own, examines physical systems that can usefully be modeled by equations of the first order.

Find helpful customer reviews and review ratings for First-Order Differential Equations: Volume 2, Theory and Application of Hyperbolic Systems of Quasilinear Equations at Read honest and unbiased product reviews from our users.5/5(1).

We construct global solutions for quasilinear hyperbolic systems and study their asymptotic behaviors. The systems include models of gas flows in a variable area duct and flows with a moving source.

Our analysis is based on a numerical scheme which generalizes the Glimm scheme for hyperbolic conservation by: Hyperbolic partial differential equations describe phenomena of material or wave transport in physics, biology and engineering, especially in the field of fluid mechanics.

Despite considerable progress, the mathematical theory is still strug­ gling with fundamental open problems concerning systems of such equations in multiple space dimensions. Get this from a library. Quasilinear hyperbolic systems, compressible flows, and waves. [Vishnu D Sharma] -- Filled with practical examples, this book presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications.

It emphasizes nonlinear theory and introduces some of. Hyperbolic to Parabolic Relaxation Theory for Quasilinear First Order Systems Article in Journal of Differential Equations (2) April with 26 Reads How we measure 'reads'.

Summary. Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with emphasizes nonlinear theory and introduces some of the most active research in the field.

After linking continuum mechanics and quasilinear partial differential equations, the book. quasilinear control Download quasilinear control or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get quasilinear control book now.

This site is like a library, Use search box in the widget to get ebook that you want. Filled with practical examples, Quasilinear Hyperbolic Systems, Compressible Flows, and Waves presents a self-contained discussion of quasilinear hyperbolic equations and systems with applications.

It emphasizes nonlinear theory and introduces some of the most active research in the link. The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with "slow" decay initial : Wen-Rong Dai.

where is replaced by and is a symmetric operator. Using energy inequalities (cf. Energy inequality) and an iteration method, the existence can be proved of a solution to the Cauchy problem for quasi-linear second-order systems for a single non-linear equation of arbitrary order. Since the characteristics and bicharacteristics (cf.

Bicharacteristic) for hyperbolic equations and systems are. Using a result on the existence and uniqueness of the semiglobal C1 solution to the mixed initial-boundary value problem for first order quasi-linear hyperbolic systems with general nonlinear boundary conditions, we establish the exact boundary controllability for quasi-linear hyperbolic systems if the C1 norm of initial and final states is small by:   Based on the theory of semi-global classical solutions to 1-D quasilinear hyperbolic systems, a constructive method with modules is presented to get various kinds of local exact boundary controllabilities, including the two-sided local exact boundary controllability, the one-sided local exact boundary controllability, the one-sided local exact boundary null controllability as well as the local.

The book represent a first step aimed at a large and rich subject and I hope that readers are sufficiently attracted to probe further. §P A bird’s eye view of hyperbolic equations The central theme of this book is hyperbolic partial differential equations. These equations are important for a variety of reasons.

In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n − 1 derivatives.

More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic of the equations of mechanics are hyperbolic, and so the.

Harry Bateman was a famous English mathematician. In writing this book he had endeavoured to supply some elementary material suitable for the needs of students who are studying the subject for the first time, and also some more advanced work which may be useful to men who are interested more in physical mathematics than in the developments of differential geometry and the theory of functions.

theory of quaslhnear systems of hyperbolic conservation laws allows for a relatively simple transition to the cases where the media is either amsotroplc, and exhibits a small nonlinear conduction current, or exhibits dispersive effects or relaxation phenomena It is shown m Section.

Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels.

HYPERBOLIC EQUATIONS gave a proof of the existence of the solution of a nonlinear hyperbolic equation. of second order and any number of variables.

In particular, these inequalities involve the square integrals of the derivatives of the functions u. A chapter on systems of conservation laws includes linear hyperbolic systems, quasilinear conversation laws, and the Riemann problem for \(p\)-systems.

Some parts of the book utilize Fourier series techniques or Lebesgue measure and integration, both of which are outlined in Appendices.This method of solution of () is easily extended to nonlinear equations of the form ut +aux =f(t,x,u).

() See Exercises, and for more on nonlinear equations of this form. SystemsofHyperbolicEquations We now examine systems of hyperbolic equations with constant coefficients in one space Size: 1MB.

The book begins with a consideration of pairs of quasilinear hyperbolic equations of the first order and goes on to explore multicomponent chromatography, complications of counter-current moving-bed adsorbers, the adiabatic adsorption column, Author: Hyun-Ku Rhee.