Semilinear evolution transmission problems across fractal layers

A semilinear parabolic transmission problem across either a fractal layer S or the corresponding prefractal layer S-h is studied. Local existence, uniqueness and regularity results for the mild solution, in both cases, are established as well as a sufficient condition on the initial datum for global existence is given. The asymptotic behaviour of the solutions of the approximating problems is studied. (C) 2012 Elsevier Ltd. All rights reserved