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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).
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).
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
205-223
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
- St. John's College, Oxford OX1 3JP, Great Britain
autor
- 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
- Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
- Department of Mathematics, University of Delhi, Delhi, India
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-1