On infinite dimensional systems of conservation laws of Keyfitz-Kranzer type

نویسنده

  • E.Yu. Panov
چکیده

We prove existence and uniqueness of strong generalized entropy solution to the Cauchy problem for an infinite dimensional system of Keyfitz-Kranzer type, in which the unknown vector takes its value in an arbitrary Banach space. We study the Cauchy problem for an equation ut + (φ(‖u‖)u)x = 0 (1) with initial condition u(0, x) = u0(x). (2) Here the unknown vector u = u(t, x) is defined in a half-plane Π = R+ × R, R+ = (0,+∞) and takes its values in some real Banach space X equipped with norm ‖ · ‖. We suppose that the function φ(r) ∈ C(R+) and rφ(r) → 0 as r → 0 + . (3) The initial function u0(x) ∈ L (R, X), i.e. it is an essentially bounded strongly measurable function on R. Remark that in the case when X = L(R) equation (1) can be written as the following integral-differential equation ∂ ∂t u(t, x, λ) + ∂ ∂x [

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Delta Shock Waves for a Linearly Degenerate Hyperbolic System of Conservation Laws of Keyfitz-Kranzer Type

This paper is devoted to the study of delta shockwaves for a hyperbolic systemof conservation laws of Keyfitz-Kranzer typewith two linearly degenerate characteristics.TheRiemannproblem is solved constructively.TheRiemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-...

متن کامل

Notes on Hyperbolic Systems of Conservation Laws and Transport Equations

Contents 1. Introduction 2 1.1. The Keyfitz and Kranzer system 2 1.2. Bressan's compactness conjecture 3 1.3. Ambrosio's renormalization Theorem 4 1.4. Well–posedness for the Keyfitz and Kranzer system 5 1.5. Renormalization conjecture for nearly incompressible BV fields 6 1.6. Plan of the paper 7 2. Preliminaries 8 2.1. Notation 8 2.2. Measure theory 9 2.3. Approximate continuity and approxima...

متن کامل

Self-similar solutions‎ ‎of the Riemann problem for two-dimensional systems of conservation‎ ‎laws

In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem

متن کامل

Some new well-posedness results for continuity and transport equations, and applications to the chromatography systems

We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of vector fields with bounded compression and possibly having a blow-up of the BV norm at the initial time. We apply these results, valid in any space dimension, to a 2×2 system of conservation laws in one...

متن کامل

Euler-Lagrange change of variables in conservation laws

We introduce a new method for studying the Cauchy problem for systems of conservation laws in one space dimension. This method is based on the equivalence of the Cauchy problems in Eulerian and Lagrangian coordinates, as regards the existence and uniqueness of entropy solutions. The main idea is to solve the problem in Lagrangian coordinates and determine the transformation linking the two coor...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005