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arXiv · 2205.06656

Dynamic boundary conditions for time dependent fractional operators on extension domains

Simone Creo·Maria Rosaria Lancia
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Abstract

We consider a parabolic semilinear non-autonomous problem $(\tilde P)$ for a fractional time dependent operator $\mathcal{B}^{s,t}_\Omega$ with Wentzell-type boundary conditions in a possibly non-smooth domain $\Omega\subset\mathbb{R}^N$. We prove existence and uniqueness of the mild solution of the associated semilinear abstract Cauchy problem $(P)$ via an evolution family $U(t,\tau)$. We then prove that the mild solution of the abstract problem $(P)$ actually solves problem $(\tilde P)$ via a generalized fractional Green formula.

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Simone Creo, Maria Rosaria Lancia. 2022-05-13. Dynamic boundary conditions for time dependent fractional operators on extension domains. https://arxiv.org/abs/2205.06656

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