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

Shangquan Bu. "Well-posedness of second order degenerate differential equations in vector-valued function spaces." Studia Mathematica 214.1 (2013): 1-16. <http://eudml.org/doc/285678>.

@article{ShangquanBu2013,
abstract = {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 $L^\{p\}(,X)$, periodic Besov spaces $B_\{p,q\}^\{s\}(,X)$ and periodic Triebel-Lizorkin spaces $F_\{p,q\}^\{s\}(,X)$, 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 $M = I_\{X\}$.},
author = {Shangquan Bu},
journal = {Studia Mathematica},
keywords = {vector-valued Fourier multipliers; -bounded operators; degenerate differential equation; wellposedness},
language = {eng},
number = {1},
pages = {1-16},
title = {Well-posedness of second order degenerate differential equations in vector-valued function spaces},
url = {http://eudml.org/doc/285678},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Shangquan Bu
TI - Well-posedness of second order degenerate differential equations in vector-valued function spaces
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 1
SP - 1
EP - 16
AB - 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 $L^{p}(,X)$, periodic Besov spaces $B_{p,q}^{s}(,X)$ and periodic Triebel-Lizorkin spaces $F_{p,q}^{s}(,X)$, 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 $M = I_{X}$.
LA - eng
KW - vector-valued Fourier multipliers; -bounded operators; degenerate differential equation; wellposedness
UR - http://eudml.org/doc/285678
ER -