Well-posedness of second order degenerate differential equations in vector-valued function spaces

• Autorzy: Shangquan Bu
• Języki publikacji: EN

Abstrakty

EN

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 $L^{p}(𝕋,X)$, 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 operators in a Banach space X satisfying D(A) ⊂ D(M). Our results generalize the previous results of W. Arendt and S. Q. Bu when $M = I_{X}$.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 47D06: One-parameter semigroups and linear evolution equations
• 42A45: Multipliers
• 47A50: Equations and inequalities involving linear operators, with vector unknowns
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 1
• Strony: 1-16

Daty

wydano

2013

Twórcy

autor

Shangquan Bu

• Department of Mathematical Science, University of Tsinghua, Beijing 100084, China

Identyfikatory

DOI

10.4064/sm214-1-1