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Maximal space regularity for abstract linear non-autonomous parabolic equations. (English) Zbl 0563.47028
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.
Reviewer: J.de Graaf

47D03 Groups and semigroups of linear operators
46M35 Abstract interpolation of topological vector spaces
35K55 Nonlinear parabolic equations
Full Text: DOI
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