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). Our results generalize the previous results of W. Arendt and S. Q. Bu when .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-1,
author = {Shangquan Bu},
title = {Well-posedness of second order degenerate differential equations in vector-valued function spaces},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {1-16},
zbl = {1277.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-1}
}
Shangquan Bu. Well-posedness of second order degenerate differential equations in vector-valued function spaces. Studia Mathematica, Tome 215 (2013) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-1-1/