Nonsmoothing in a single conservation law with memory

It is shown that, provided the nonlinearity $sigma$ is strictly convex, a discontinuity in the initial value $u_0(x)$ of the solution of the equation $$ {partial over partial t} Big( u(t,x) + int_0^t k(t-s) (u(s,x)-u_0(x)),ds Big) + sigma(u)_x(t,x) = 0, $$ where $t>0$ and $xin mathbb{R}$, is not...

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Bibliographic Details
Main Author: G. Gripenberg
Format: Article
Published: Texas State University 2001-01-01
Series:Electronic Journal of Differential Equations
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