Beyond quenching for degenerate singular semilinear parabolic equations

Let q be a nonzero real constant greater than -1, D = (0, a), Ohm = D x (0, infinity), (D) over bar and <(<Ohm>)over bar> be their respective closures, Lu = x(q)u(t) - u(xx), and chi (s) = {(1 if u is an element ofS,)(0 if u is not an element ofS) be the characteristic function of the set S. Beyond quenching is studied for the problem, u(x,t) is an element of C-2,C-1 ({u < c} boolean AND Ohm) boolean AND C-1,C-0(Ohm) boolean AND C(<(<Ohm>)over bar>), u less than or equal to c in Ohm, and that every element of the omega -limit set obtained from the minimal weak solution (among solutions obtained via regularization) is a weak steady-state solution. (C) 2001 Elsevier Science Inc. All rights reserved.