ON THE PROFILE OF SOLUTIONS WITH TIME-DEPENDENT SINGULARITIES FOR THE HEAT EQUATION

Let N >= 2, T is an element of(0, infinity] and xi is an element of C(0, T;R-N). Under some regularity condition for xi it is known that the heat equation u(t) - Delta u = 0, x is an element of R-N\{xi(t)}, t is an element of (0, T) has a solution behaving like the fundamental solution of the Laplace equation as x -> xi(t) for any fixed t. In this paper we construct a singular solution whose behavior near x = xi(t) suddenly changes from that of the fundamental solution of the Laplace equation at some t.