Geodesic
Nonsmoothing in a single conservation law with memory
Electronic Journal of Differential Equations, Tome 2001 (2001).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a140,
     author = {Gripenberg, G.},
     title = {Nonsmoothing in a single conservation law with memory},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2001},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a140/}
}
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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__a140/