Irregular Heat Flow Problems
Maria Rosaria Lancia, Paola Vernole · SIAM Journal on Mathematical Analysis · 2010
We study a nonsteady transmission problem across either a fractal layer S or the corresponding prefractal layer $S_h$. The transmission condition is of order two. Existence, uniqueness, and regularity results for the strict solution, in both cases, are established as well as convergence results for the solutions of the approximating problems in varying Hilbert spaces.