TITLE:
Semilinear Venttsel’ Problems in Fractal Domains
AUTHORS:
Maria Rosaria Lancia, Paola Vernole
KEYWORDS:
Energy Forms, Fractal Domains, Trace Theorems, Semigroups, Semilinear Parabolic Equations
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.12,
June
26,
2014
ABSTRACT: We study a semilinear parabolic problem with a semilinear dynamical
boundary condition in an irregular domain with fractal boundary. Local
existence, uniqueness and regularity results for the mild solution, are
established via a semigroup approach. A sufficient condition on the initial datum
for global existence is given.