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Maximal regularity for second order non-autonomous Cauchy problems

Tom 189 / 2008

Charles J. K. Batty, Ralph Chill, Sachi Srivastava Studia Mathematica 189(2008), 205-223 MSC: Primary 47E05; Secondary 34G10, 35B65, 47D09. DOI: 10.4064/sm189-3-1


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 $A(t) = \kappa B(t)$.


  • Charles J. K. BattySt. John's College
    Oxford OX1 3JP, Great Britain
  • 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
  • Sachi SrivastavaDepartment of Mathematics
    Indian Institute of Science
    Bangalore 560 012, India
    Current address:
    Department of Mathematics
    University of Delhi
    Delhi, India

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