Maximal regularity for second order non-autonomous Cauchy problems

• Autorzy: Charles J. K. Batty , Ralph Chill , Sachi Srivastava
• Języki publikacji: EN

Abstrakty

EN

We consider some non-autonomous second order Cauchy problems of the form
ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0.
We assume that the first order problem
u̇ + B(t)u = f(t ∈ [0,T]), 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(t₁) and A(t₂) always coincide, or when A(t) = κB(t).

Kategorie tematyczne

• 47D09: Operator sine and cosine functions and higher-order Cauchy problems
• 34G10: Linear equations
• 35B65: Smoothness and regularity of solutions
• 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 189
• Numer: 3
• Strony: 205-223

Daty

wydano

2008

Twórcy

autor

Charles J. K. Batty

• St. John's College, Oxford OX1 3JP, Great Britain

autor

Ralph Chill

• Laboratoire de Mathématiques et Applications de Metz - CNRS, Université Paul Verlaine - Metz, UMR 7122, Bât. A, Île du Saulcy, 57045 Metz Cedex 1, France

autor

Sachi Srivastava

• Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
• Department of Mathematics, University of Delhi, Delhi, India

Identyfikatory

DOI

10.4064/sm189-3-1