Last edited by Meztisida
Monday, August 3, 2020 | History

5 edition of Generalized Characteristics of First Order PDEs: found in the catalog.

Generalized Characteristics of First Order PDEs:

Applications in Optimal Control and Differential Games

by Arik Melikyan

  • 214 Want to read
  • 1 Currently reading

Published by Birkhauser .
Written in English

    Subjects:
  • Applied mathematics,
  • Differential Equations,
  • Game theory,
  • Differential equations, Partial,
  • Partial Differential Equations,
  • Mathematics,
  • Science/Mathematics,
  • Differential games,
  • Differential Equations - Partial Differential Equations,
  • First Order PDEs,
  • Mathematics / Differential Equations,
  • Control Theory,
  • Differential equations, Partia

  • The Physical Object
    FormatHardcover
    Number of Pages332
    ID Numbers
    Open LibraryOL8074608M
    ISBN 100817639845
    ISBN 109780817639846

    Nonlinear first-order PDE. Characteristics 1. Basic notions: derivatives and multi-index, support of a function, smoothness of a boundary of domain, integration by parts, classification of PDE w.r.t. (non)linearity. 2. General setting of first-order PDE. Example: physical derivation of the conservation law. 3. Characteristic equations. Meaning of a rst order PDE and its solution In this article we shall consider uto be a real function of two real independent variables xand Dbe a domain in (x,y)-plane and ua real valued function defined on D: u: D→ R, D⊂ R2 De nition A first order partial differential equation is a File Size: KB.

      Generalized Characteristics of First Order PDEs: Applications in 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/5(56).   Generalized Characteristics of First Order PDEs: Applications in 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 : Chongying Dong.

    22 2. First-Order PDEs This last statement is an example of a conservation law and it is quite general. If we assume the time derivative and integral commute, (we will investigate in great detail later), we get Zx x0 ρt(s, t)ds = q(x0,t)−q(x,t), whereρt is shorthand for∂ρ/∂t. File Size: KB. LinearChange ofVariables TheMethodof Characteristics Summary Summary Consider a first order PDE of the form A(x,y) ∂u ∂x +B(x,y) ∂u ∂y = C(x,y,u). (5) When A(x,y) and B(x,y) are constants, a linear change of variables can be used to convert (5) into an “ODE.” In general, the method of characteristics yields a system of ODEs.


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Generalized Characteristics of First Order PDEs: by Arik Melikyan Download PDF EPUB FB2

Generalized Characteristics of First Order PDEs Applications in Optimal Control and Differential Games. Authors: Melikyan, Arik Free Preview. Generalized Characteristics of First Order PDEs: Applications in Optimal Control and Differential Games - Kindle edition by Melikyan, Arik.

Download it once and read it on your Kindle device, PC, phones or by: In some domains of mechanics, Generalized Characteristics of First Order PDEs: book 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). Generalized Solutions of First Order PDEs Generalized Characteristics of First-Order PDE’s. Generalized Solutions of First Order PDEs Book Subtitle The Dynamical Optimization Perspective Authors.

Andrei I. Subbotin; Series Title Systems & Control: Foundations & Applications. In the present chapter we introduce the notion of minimax solution to first-order partial differential equation. The proposed definition is based on the weak invariance property of the graph of a generalized solution with respect to a system of differential inclusions, which will be called characteristic by: 1.

This book concerns the extension of the method of characteristics in the following cases: (i) the generalized solution is nonsmooth while the Hamiltonian may be either smooth or nonsmooth; (ii) the solution is smooth (classical) but the Hamiltonian is nonsmooth; (iii) the PDE is the quasilinear second order Euler equation of a variational.

Generalized Solutions of First Order PDEs The Dynamical Optimization Perspective. Generalized Characteristics of First-Order PDE’s. Andreĭ I. Subbotin. Pages Pages Differential Games. Andreĭ I. Subbotin. Pages Boundary-Value Problems for First-Order PDE’s.

Andreĭ I. Subbotin. Pages Back Matter. Melikyan A. () Generalized Solutions and Singular Characteristics of First Order PDEs. In: Generalized Characteristics of First Order PDEs. Birkhäuser, Boston, MAAuthor: Arik Melikyan. FIRST ORDER PDES CRISTIAN E. GUTIERREZ´ FEBRUARY 3, Contents 1.

Quasi-linear equations 2 Step 1 2 Step 2 2 Cauchy problem 3 2. Degenerate case 4. It turns out that we can generalize the method of characteristics to the case of so-called quasilinear 1st order PDEs: u t +c(x;t;u)u x = f(x;t;u); u(x;0)=u 0(x) (6) Note that now both the left hand side and the right hand side may contain nonlinear terms.

Assume that u(x;t) is a solution of the initial value problem (6).File Size: KB. Generalized Characteristics of First Order PDEs: Applications in Optimal Control and Differential Games by Arik Melikyan English | | ISBN: | Pages | DJVU | MB In some domains of mechanics, physics and control theory boundary value problems arise for.

Book Reviews A. Melikyan: Generalized Characteristic of First Order PDEs. Applications in Optimal Control and Differential Games. Birkhäuser, Boston,xiv+ pages, ISBNprice DM ,–. Šárka Matušů-NečasováAuthor: Šárka Matušů-Nečasová.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Generalized Solutions of First Order PDEs: The Dynamical Optimization Perspective (Systems & Control: Foundations & Applications).Manufacturer: Birkhäuser.

First Order Partial Differential Equations “The profound study of nature is the most fertile source of mathematical discover-ies.” - Joseph Fourier () Introduction We begin our study of partial differential equations with first order partial differential equations.

Before doing. First Order PDEs Characteristics The Simplest Case Suppose u(x,t)satisfies the PDE aut +bux =0 where b,c are constant. If a =0, the PDE is trivial (it says that ux =0 and so u = f(t). If a 6= 0, it reduces to ut +cux =0 where c =b/a. () We know from § that the solution is f(x −ct).

This represents a wave travelling in the xFile Size: 89KB. Generalized Solutions of First Order Pdes by Subbotin, Andrei I.

ISBN ISBN10 In this book, the authors present another approach that can be considered as a non-classical method of characteristics, according to which the generalized solution (called the minimax solution) is assumed to be weak invariant with respect to the.

First order PDE: The Methods of Characteristics. John Andersson, [email protected] Septem 1 Brie y about the course. This course consists of three parts and these notes are only the theoretical aspects of the rst part.

But since these notes introduce the rst part it might be in order. LinearChange ofVariables TheMethodof Characteristics Summary Summary Consider a first order PDE of the form A(x,y) ∂u ∂x +B(x,y) ∂u ∂y = C(x,y,u).

(5) When A(x,y) and B(x,y) are constants, a linear change of variables can be used to convert (5) into an “ODE.” In general, the method of characteristics yields a system of ODEs equivalent to (5).File Size: 1MB.

Generalized Characteristics of First Order PDEs: Applications in Optimal Control and Differential Games. [Arik Melikyan] -- In some domains of mechanics, physics and control theory boundary value problems arise for nonlinear first order PDEs.

GENERALIZED SOLUTIONS TO FIRST-ORDER PDEs In some domains of Control Theory, Mechan­ics and Physics the boundary-value problems in terms of nonlinear first-order PDE may arise of the form: F(x, u(x), p(x)) =0, x Enc Rn (1) u(x) = w (X), X E M C an Here u(x) is the unknown function, w(x) IS its boundary value, p =: Arik A.

Melikyan. Systems of First Order PDEs • For an ODE (1) u0(x)=f(x,u(x)), we found that the existence of solutions was no harder to prove for a function u: R → Rn than it was for the case of a function u: R → R. – Namely, we could consider (1) to be a system of equations.Connections between Optimal Control Problems and Generalized Solutions of PDEs of the First Order.

Author links open overlay panel Ekaterina A. Kolpakova Nina N. Subbotina * Show moreAuthor: Ekaterina A. Kolpakova, Nina N. Subbotina.Generalized characteristics of first order PDEs: applications in optimal control and differential games.