On existence and regularity of a terminal value problem for the time fractional diffusion equation
https://doi.org/10.1088/1361-6420/ab730dPublisher, magazine: ,
Publication year: 2020
Lưu Trích dẫn Chia sẻAbstract
In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of ${\mathbb{R}}^{k}$, k ≥ 1, which includes the fractional power ${\mathcal{L}}^{\beta }$, 0 < β ≤ 1, of a symmetric uniformly elliptic operator $\mathcal{L}$ defined on L2(D). A representation of solutions is given by using the Laplace transform and the spectrum of ${\mathcal{L}}^{\beta }$. We establish some existence and regularity results for our problem in both the linear and nonlinear case.
Tags: Existence; Uniqueness; Regularity; Final value problem; time fractional derivative
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