an:03897652
Zbl 0563.47028
Acquistapace, Paolo; Terreni, Brunello
Maximal space regularity for abstract linear non-autonomous parabolic equations
EN
J. Funct. Anal. 60, 168-210 (1985).
00149952
1985
j
47D03 46M35 35K55
linear non-autonomous Cauchy problem; infinitesimal operator of an analytic semigroup; abstract regularity; interpolation spaces
Let E be a Banach space and \(\{\) A(t)\(\}\), \(t\in [0,T]\) a family of closed linear operators in E. The authors study the linear non-autonomous Cauchy problem
\[
u'(t)-A(t)u(t)=f(t)\quad for\quad t\in [0,T],\quad u(0)=x,\quad x\in E,\quad f\in C([0,T],E);
\]
A(t) is the infinitesimal operator of an analytic semigroup, not necessarily strongly continuous at 0, with domains not depending on t. The abstract regularity is studied by means of interpolation spaces.
J.de Graaf