Radon measure-valued solutions of first order scalar conservation laws
نویسندگان
چکیده
منابع مشابه
Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws
Entropy solutions have beenwidely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (AnnMath 170(3):1417–1436, 2009) and Chiodaroli et al. (2013) have demonstrated that entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical sc...
متن کاملVariational properties of the kinetic solutions of scalar conservation laws
We consider the variational kinetic formulation of the Cauchy problem for a scalar conservation law due to Brenier[] and Panov[]. The solutions in this formulation are represented by a kinetic density function Y that solves a certain differential inclusion ∂tY ∈ A(Y ), in a suitable Hilbert space. In this paper we establish a sufficient “nondegeneracy” condition under which the operator A is th...
متن کاملError Estimates of Approximate Solutions for Nonlinear Scalar Conservation Laws
There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...
متن کاملStructure of Entropy Solutions for Multi{dimensional Scalar Conservation Laws
An entropy solution u of a multi{dimensional scalar conservation law is not necessarily in BV , even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV {function in the sense that the shock location is codimension{one rectiiable. This result highlights the regularizing eeect of genuine non-linearity in a qualitative way; it is based on the loca...
متن کاملOn weak convergence of entropy solutions to scalar conservation laws
We prove that weak limits of entropy solutions to a one-dimensional scalar conservation law are entropy solutions as well. We consider a scalar conservation law ut + f(u)x = 0, (t, x) ∈ Π = (0, +∞)× R. (1) The flux function f(u) is supposed to be only continuous: f(u) ∈ C(R). Recall the notion of an entropy solution of (1) in the sense of Kruzhkov [6]. Definition 1. A bounded measurable functio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Nonlinear Analysis
سال: 2018
ISSN: 2191-950X
DOI: 10.1515/anona-2018-0056