NONSMOOTHING IN A SINGLE CONSERVATION LAW WITH MEMORY

It is shown that, provided the nonlinearity a is strictly convex, a discontinuity in the initial value uo(x) of the solution of the equation partial derivative/partial derivative t (u(t, x) + integral(t)(0) u(t x) + f k(t s)(u(s, x) uo(x)) ds) + 0-(u) (t, x) = 0, 0 where t > 0 and x E R, is not immediately smoothed out even if the memory kernel k is such that the solution of the problem where a is a linear function is continuous for t > 0.