论文标题
扩展域上时间依赖分数操作员的动态边界条件
Dynamic boundary conditions for time dependent fractional operators on extension domains
论文作者
论文摘要
我们考虑一个抛物线半联联问题$（\ tilde p）$ $（\ tilde p）$，用于分数时间依赖的操作员$ \ Mathcal {b}^{s，t}^{s，t}_Ω$，在可能的非平滑型域$ type边界条件下，可能是非平滑的域$ chaun $ ch \ subset $ω\ subset \ subset \ subset \ subset \ subset \ mathbbbb {r}^n $。我们证明了通过进化家庭$ u（t，τ）$的相关半线性抽象问题$（p）$的温和解决方案的存在和独特性。然后，我们证明抽象问题的温和解决方案$（p）$实际上通过广义的分数绿色公式解决了问题$（\ tilde p）$。
We consider a parabolic semilinear non-autonomous problem $(\tilde P)$ for a fractional time dependent operator $\mathcal{B}^{s,t}_Ω$ with Wentzell-type boundary conditions in a possibly non-smooth domain $Ω\subset\mathbb{R}^N$. We prove existence and uniqueness of the mild solution of the associated semilinear abstract Cauchy problem $(P)$ via an evolution family $U(t,τ)$. We then prove that the mild solution of the abstract problem $(P)$ actually solves problem $(\tilde P)$ via a generalized fractional Green formula.
