Free boundary layer formation in nonlinear heat propagation

We investigate a phenomenon of boundary layer formation which occurs for la rge times near the free boundary of nonnegative solutions to the nonlinear heat-conduction equation with absorption u(t) = (u(m))(xx) - u(p) in Q = R x (0,infinity), with parameters 1 < p < m. The large-time behaviour of u must be described by matched asymptotics. There is a regular region inside the support where the solution becomes asymptotically flat, and a thin boundary layer near th e free boundary, with a universal development given by a self-similar solut ion.