Well-posedness of fractional degenerate differential equations with finite delay on vector-valued functional spaces

作者：Bu, Shangquan; Cai, Gang^*

来源：Mathematische Nachrichten, 2018, 291(5-6): 759-773.

DOI：10.1002/mana.201600502

• Well-posedness
• fractional degenerate differential equation
• Fourier multiplier
• vector-valued function spaces

We study the well- posedness of the fractional degenerate differential equations with finite delay (P-alpha) : D-alpha (Mu)(t) = Au(t) + Fu(t) + f (t), ( 0 <= t <= 2 pi, alpha > 0) on Lebesgue- Bochner spaces L-p (T; X), periodic Besov spaces B-p,q(s) (T; X) and periodic Triebel- Lizorkin spaces F-p,q(s) (T; X), where A and M are closed linear operators on a Banach space X satisfying D(A) subset of D(M), F is a bounded linear operator from L-p ([-2 pi, 0]; X) ( resp. B-p,q(s) ([-2 pi, 0]; X) and F-p,q(s) ([-2 pi, 0]; X)) into X, where u(t) is given by u(t)(s) = u(t + s) when s is an element of [-2 pi, 0] and t is an element of [0, 2 pi]. Using known operator-valued Fourier multiplier theorems, we give necessary or sufficient conditions for the well- posedness of (P-alpha) in the above three function spaces.

• 出版日期2018-4
• 单位清华大学; 重庆师范大学