Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form ü + B(t)̇ + A(t)u = f (t ∈ [0, T]), u(0) = ̇(0) = 0. We assume that the first order problem ü + B(t)u = f (t∈ [0, T]), u(0) = 0, has Lp-maximal regularity. Then we establish Lp-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). © Instytut Matematyczny PAN, 2008.