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1998 | 130 | 3 | 263-274
Tytuł artykułu

Time-dependent perturbation theory for abstract evolution equations of second order

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A condition on a family ${B(t):t ∈ [0,T]}$ of linear operators is given under which the inhomogeneous Cauchy problem for u"(t)=(A+ B(t))u(t) + f(t) for t ∈ [0,T] has a unique solution, where A is a linear operator satisfying the conditions characterizing infinitesimal generators of cosine families except the density of their domains. The result obtained is applied to the partial differential equation $$ u_{tt} = u_{xx} + b(t,x)u_x(t,x) + c(t,x)u(t,x) + f(t,x) for (t,x) ∈ [0,T]×[0,1], u(t,0) = u(t,1) = 0 for t ∈ [0,T], u(0,x) = u_0(x), u_t(0,x) = v_0(x) for x ∈ [0,1] $$ in the space of continuous functions on [0,1].
Słowa kluczowe
Czasopismo
Rocznik
Tom
130
Numer
3
Strony
263-274
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-10-10
Twórcy
autor
  • Department of System Science, Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
Bibliografia
  • [1] G. Da Prato and E. Sinestrari, Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa 14 (1987), 285-344.
  • [2] J. Kisyński, On cosine operator functions and one-parameter groups of operators, Studia Math. 44 (1972), 93-105.
  • [3] D. Lutz, On bounded time-dependent perturbation of operator cosine functions, Aequationes Math. 23 (1981), 197-203.
  • [4] I. Miyadera, S. Oharu and N. Okazawa, Generation theorems of semi-groups of linear operators, Publ. RIMS Kyoto Univ. 8 (1973), 509-555.
  • [5] H. Oka, Integrated resolvent operators, J. Integral Equations Appl. 7 (1995), 193-232.
  • [6] H. Serizawa and M. Watanabe, Perturbation for cosine families in Banach spaces, Houston J. Math. 12 (1986), 117-124.
  • [7] H. Serizawa and M. Watanabe, Time-dependent perturbation for cosine families in Banach spaces, ibid., 579-586.
  • [8] M. Sova, Cosine operator functions, Rozprawy Mat. 49 (1966).
  • [9] N. Tanaka, Quasilinear evolution equations with non-densely defined operators, Differential Integral Equations 9 (1996), 1067-1106.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv130i3p263bwm
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