Quenching behavior for degenerate parabolic problems

This article studies the degenerate parabolic differential equation, u(xx) - x(q)u(t) = -f (u), where q is any real number and f is an element of C-2 (0, c) for some constant c such that f (0) > 0, f' > 0, f" greater than or equal to 0 and lim(u -->c)- f (u) = infinity. With nonnegative initial data and aero boundary condition, location of quenching and conditions for sing le-point quenching are discussed. An upper bound for quenching time for sin gle-point quenching is also established.