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

• Autorzy: Yuhua Lin
• 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].

Kategorie tematyczne

• 47D09: Operator sine and cosine functions and higher-order Cauchy problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 3
• Strony: 263-274

Daty

wydano

1998

otrzymano

1997-10-10

Twórcy

autor

Yuhua Lin

• Department of System Science, Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan

Bibliografia

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