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.
Highlights
In this paper we study a semilinear problem in a fractal domain with semilinear dynamical boundary conditions
We study the problem by a semigroup approach
As to the regularity of w, taking into ( ) account that J (u (⋅,t )) ∈ L2 (Ω) from Theorem 1.3 in [44] part B, it follows that w ∈ C 3 Ω , this concludes the proof
Summary
In this paper we study a semilinear problem in a fractal domain with semilinear dynamical boundary conditions. We stress the fact that it is not neither known a characterization of the domain of the fractal Laplacian ∆F To overcome this difficulty we adapt the abstract approach in [18] to prove local existence and uniqueness results for the mild solution.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
