EXTINCTION PROPERTIES OF SEMILINEAR HEAT-EQUATIONS WITH STRONG ABSORPTION

Consider the initial-boundary value problem for u//t equals DELTA u - lambda u**q with lambda greater than 0, 0 less than q less than 1; the initial data are nonnegative and the boundary data vanish. It is well known that the solution becomes extinct in finite time T, i. e. , u(x,t) becomes identically zero for t greater than equivalent to T, where T is some positive number. In this paper we study the profile of x approaching u(x, t) as t approaches T.