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.
@article{urn:eudml:doc:44508,
title = {Fundamental solutions and singular shocks in scalar conservation laws.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {16},
year = {2003},
pages = {443-463},
zbl = {1057.35002},
mrnumber = {MR2032927},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44508}
}
Chasseigne, Emmanuel. Fundamental solutions and singular shocks in scalar conservation laws.. Revista Matemática de la Universidad Complutense de Madrid, Tome 16 (2003) pp. 443-463. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44508/