We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has -maximal regularity. Then we establish -maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-1,
author = {Charles J. K. Batty and Ralph Chill and Sachi Srivastava},
title = {Maximal regularity for second order non-autonomous Cauchy problems},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {205-223},
zbl = {1166.47046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-1}
}
Charles J. K. Batty; Ralph Chill; Sachi Srivastava. Maximal regularity for second order non-autonomous Cauchy problems. Studia Mathematica, Tome 187 (2008) pp. 205-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-1/