Geodesic
Nonsmoothing in a single conservation law with memory
Electronic journal of differential equations, Tome 2001 (2001)
It is shown that, provided the nonlinearity

$ {\partial \over \partial t} \Big( u(t,x) + \int_0^t k(t-s) (u(s,x)-u_0(x))\,ds \Big) + \sigma(u)_x(t,x) = 0, $

where $t greater than 0$ and $x\in \mathbb{R}$, is not immediately smoothed out even if the memory kernel $k$ is such that the solution of the problem where $\sigma$ is a linear function is continuous for $t greater than 0$.
Classification : 35L65, 35L67, 45K05
Keywords: conservation law, discontinuous solution, memory 
@article{EJDE_2001__2001__a62,
     author = {Gripenberg,  G.},
     title = {Nonsmoothing in a single conservation law with memory},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0963.35118},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a62/}
}
TY  - JOUR
AU  - Gripenberg,  G.
TI  - Nonsmoothing in a single conservation law with memory
JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
UR  - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a62/
LA  - en
ID  - EJDE_2001__2001__a62
ER  - 
%0 Journal Article
%A Gripenberg,  G.
%T Nonsmoothing in a single conservation law with memory
%J Electronic journal of differential equations
%D 2001
%V 2001
%U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a62/
%G en
%F EJDE_2001__2001__a62
Gripenberg,  G. Nonsmoothing in a single conservation law with memory. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a62/