On the Long-time Behaviour of Solutions to a Conservation Law with Memory

We show that any solution of the scalar conservation law (u+k*u)_t+σ(u)_x=0 starting from spatially periodic initial datum stabilizes to its integral mean as time goes to infinity. No convexity or ‘genuinely non-linear’ like conditions are assumed concerning σ. © 1997 by B. C. Teubner stuttgart–John Wiley & Sons Ltd.