Quenching phenomena in strongly degenerate diffusion equations with strong absorption

We examine the degenerate parabolic equation ut = upuxx − u−qχ{u>0} with boundary value u|∂Ω = 1 in a bounded real interval Ω, wherep >1 and q ∈ (−1,p−1). When investigating the evolution of the dead core set {u(t ) = 0}, we find that the two regimes q < 1 − p and q >1 − p show completely different behavior. Finally, we rule out the possibility of quenching in infinite time under certain assumptions on p, q and the size of Ω.  2003 Elsevier Inc. All rights reserved.