STABILITY OF A FRONT FOR A NONLOCAL CONSERVATION LAW

We study the stability of a front for the law 2w(t) - (w(x) - gamma(1 - w(2))(Kw)(x))(x) = 0. It was proved by Del Passe and De Mottoni tha t an increasing stationary solution, u, exists. We show that it is sta ble in the following sense: there is epsilon > 0 such that if w(0) = u + v with \v\(2) < epsilon, then there is alpha(t) differentiable such that w(x, t) = u(alpha(t) + x) + v(x, t) and sup(R)\v(x, t)\ converge s to 0 as t goes to infinity. Also, if v is initially odd, alpha(t) = 0.