Quenching for nonlinear degenerate parabolic problems

For the problem given by u τ = ( ξ r u m u ξ ) ξ / ξ r + f ( u ) for 0 < ξ < a , 0 < τ < Λ ≤ ∞ , u ( ξ , 0 ) = u 0 ( ξ ) for 0 ≤ ξ ≤ a , and u ( 0 , τ ) = 0 = u ( a , τ ) for 0 < τ < Λ , where a and m are positive constants, r is a constant less than 1, f ( u ) is a positive function such that lim u → c − f ( u ) = ∞ for some positive constant c , and u 0 ( ξ ) is a given function satisfying u 0 ( 0 ) = 0 = u 0 ( a ) , this paper studies quenching of the solution u .