LOCAL AND GLOBAL PROPERTIES OF SOLUTIONS OF HEAT EQUATION WITH SUPERLINEAR ABSORPTION

We study the limit when k -> infinity of the solutions of partial derivative(t)u - Delta u + f(u) = 0 in R-N x (0, infinity) with initial data k delta, when f is a positive superlinear increasing function. We prove that there exist essentially three types of possible behaviour according to whether f(-1) and F-1/2 belong or not to L-1 (1, infinity), where F (t) = f(0)(t) f (s)ds. We use these results for providing a new and more general construction of the initial trace and some uniqueness and nonuniqueness results for solutions with unbounded initial data.