# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Maximal regularity for second order non-autonomous Cauchy problems

### Tom 189 / 2008

Studia Mathematica 189 (2008), 205-223 MSC: Primary 47E05; Secondary 34G10, 35B65, 47D09. DOI: 10.4064/sm189-3-1

#### Streszczenie

We consider some non-autonomous second order Cauchy problems of the form $$\ddot u + B(t) \dot u + A(t) u = f \quad (t\in [0,T]) , \ \quad u(0) = \dot u (0) =0.$$ We assume that the first order problem $$\dot u + B(t) u = f \quad (t\in [0,T]) , \ \quad u(0) =0,$$ has $L^p$-maximal regularity. Then we establish $L^p$-maximal regularity of the second order problem in situations when the domains of $B(t_1)$ and $A(t_2)$ always coincide, or when $A(t) = \kappa B(t)$.

#### Autorzy

• Charles J. K. BattySt. John's College
Oxford OX1 3JP, Great Britain
e-mail
• Ralph ChillLaboratoire de Mathématiques
et Applications de Metz – CNRS
Université Paul Verlaine – Metz
UMR 7122, Bât. A, Île du Saulcy
57045 Metz Cedex 1, France
e-mail
Indian Institute of Science
Bangalore 560 012, India
Department of Mathematics
University of Delhi
Delhi, India
e-mail

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