Quenching for degenerate semilinear parabolic equations

Abstract

Let q and a be nonzero constants, and for some constant c such that . We show existence of a unique classical solution for the degenerate parabolic differential equation,, subject to the initial condition and the boundary conditionsu. Let . It is established that if M>∞, then the set of quenching points is in for q>0, and in for q>0. At each quenching point, it is shown that u_t bows up. The critical length is proved to be the same as that for q=0. A comparison of the quenching time with that for q=0 is also given.

Keywords:

• Classical solutions
• quenching phenomena