Generic blow-up behavior of solutions of one-dimensional semilinear parabolic problems

Abstract

We consider the Cauchy problem (1) u(t) = u(xx) + u(p); x Є R, t > 0, p > 1 (2) u(x, 0) = u0 (x), x Є R, where u0(x) is continuous, nonnegative and bounded. Assume that the solution u(x, t) of (1), (2) blows up at x = 0, t = T. We describe here the generic asymptotic behaviour of u(x, t) as (x, t) approaches (0, T).