Fundamental solutions and singular shocks in scalar conservation laws.

Chasseigne, 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 -