Semilinear Venttsel’ Problems in Fractal Domains

Maria Rosaria Lancia, Paola Vernole

Dipartimento di Matematica, Università degli Studi di Roma “La Sapienza”, Roma, Italy.
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università degli Studi di Roma “La Sapienza”, Roma, Italy.

DOI: 10.4236/am.2014.512175                

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.

Keywords

Energy Forms, Fractal Domains, Trace Theorems, Semigroups, Semilinear Parabolic Equations

Conflicts of Interest

The authors declare no conflicts of interest.

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