POINTWISE DECAY FOR THE SOLUTIONS OF DEGENERATE AND SINGULAR PARABOLIC EQUATIONS

We study the asymptotic behavior, as t --> infinity, of the solutions to the evolutionary p-Laplace equation v(t) = div(|del v|(p-2)del v), with tine-independent lateral boundary values. We obtain the sharp decay rate of max(x is an element of Omega)|v(x, t) - u(x)|, where u is the stationary solution, both in the degenerate case p > 2 and in the singular case 1 < p < 2. A key tool in the proofs is the Moser iteration, which is applied to the difference v(x, t) - u(x). In the singular case, we construct all example proving that the celebrated phenomenon of finite extinction time, valid for v(x, t) when u equivalent to 0, does not have a counterpart for v(x, t) - u(x).