Free boundary layer formation in nonlinear heat propagation
Manuela Yuste Chaves, J.L Vázquez · Communications in Partial Differential Equations · 1999
We investigate a phenomeno of boundary layer formation which occurs for large times near the free boundary of monnegative solutions to the nonlinear heat-conduction equation with absorption with parameters1 ≤p ≤m. The large-time behaviourf 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 the free boundary, with a universal development given by a self-similar solution