# Fundamental solutions and singular shocks in scalar conservation laws.

Revista Matemática Complutense (2003)

- Volume: 16, Issue: 2, page 443-463
- ISSN: 1139-1138

## Access Full Article

top## Abstract

top## How to cite

topChasseigne, Emmanuel. "Fundamental solutions and singular shocks in scalar conservation laws.." Revista Matemática Complutense 16.2 (2003): 443-463. <http://eudml.org/doc/44508>.

@article{Chasseigne2003,

abstract = {We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks in the theory, and the initial data also has to be understood in a generalized sense, since locally infinite measures appear.},

author = {Chasseigne, Emmanuel},

journal = {Revista Matemática Complutense},

keywords = {Ecuaciones diferenciales hiperbólicas; Teorema de existencia; Solución débil; Singularidades; Discontinuidad; Funciones convexas; entropy criterion; infinite shocks},

language = {eng},

number = {2},

pages = {443-463},

title = {Fundamental solutions and singular shocks in scalar conservation laws.},

url = {http://eudml.org/doc/44508},

volume = {16},

year = {2003},

}

TY - JOUR

AU - Chasseigne, Emmanuel

TI - Fundamental solutions and singular shocks in scalar conservation laws.

JO - Revista Matemática Complutense

PY - 2003

VL - 16

IS - 2

SP - 443

EP - 463

AB - We study the existence and non-existence of fundamental solutions for the scalar conservation laws ut + f(u)x = 0, related to convexity assumptions on f. We also study the limits of those solutions as the initial mass goes to infinity. We especially prove the existence of so-called Friendly Giants and Infinite Shock Solutions according to the convexity of f, which generalize the explicit power case f(u) = um. We introduce an extended notion of solution and entropy criterion to allow infinite shocks in the theory, and the initial data also has to be understood in a generalized sense, since locally infinite measures appear.

LA - eng

KW - Ecuaciones diferenciales hiperbólicas; Teorema de existencia; Solución débil; Singularidades; Discontinuidad; Funciones convexas; entropy criterion; infinite shocks

UR - http://eudml.org/doc/44508

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.