Nonsimultaneous quenching

AbstractWe study the possibility of nonsimultaneous quenching for positive solutions of a coupled system of two semilinear heat equations, ut = uxx − v−p, vt = vxx − u−q, p, q > 0, with homogeneous Neumann boundary conditions and positive initial data. Under some assumptions on the initial data, we prove that if p, q ≥ 1, then quenching is always simultaneous, if p < 1 or q < 1, then there exists a wide class of initial data with nonsimultaneous quenching, and finally, if p < 1 ≤ q or q < 1 ≤ p, then quenching is always nonsimultaneous. We also give the quenching rates in all cases