Well-posedness of fractional degenerate differential equations in Banach spaces
Keyword(s):
Abstract We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces $\begin{array}{} B_{p,q}^s \end{array}$ (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ and 0 < β < α are fixed. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for Lp-well-posedness and $\begin{array}{} B_{p,q}^s \end{array}$-well-posedness of above equation.
2018 ◽
Vol 61
(4)
◽
pp. 717-737
◽
2013 ◽
Vol 56
(3)
◽
pp. 853-871
◽
2016 ◽
Vol 60
(2)
◽
pp. 349-360
◽
2019 ◽
Vol 13
(07)
◽
pp. 2050124
1974 ◽
Vol 72
(1)
◽
pp. 39-55
◽
1995 ◽
Vol 58
(2)
◽
pp. 222-231