Well-posedness of second order degenerate differential equations in vector-valued function spaces
Shangquan Bu (2013)
Studia Mathematica
Similarity:
Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces , periodic Besov spaces and periodic Triebel-Lizorkin spaces , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M)....