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

Lin, Yuhua

Lin, Yuhua

Studia Mathematica, Tome 129 (1998), p. 263-274 / Harvested from The Polish Digital Mathematics Library

Résumé

A condition on a family $B (t) : t \in [0, T]$ 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 $u_{t t} = u_{x x} + b (t, x) u_{x} (t, x) + c (t, x) u (t, x) + f (t, x) f o r (t, x) \in [0, T] \times [0, 1], u (t, 0) = u (t, 1) = 0 f o r t \in [0, T], u (0, x) = u_{0} (x), u_{t} (0, x) = v_{0} (x) f o r x \in [0, 1]$ in the space of continuous functions on [0,1].

Publié le : 1998-01-01

Zbl 0916.47035

EUDML-ID : urn:eudml:doc:216557

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     author = {Yuhua Lin},
     title = {Time-dependent perturbation theory for abstract evolution equations of second order},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {263-274},
     zbl = {0916.47035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p263bwm}
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Lin, Yuhua. Time-dependent perturbation theory for abstract evolution equations of second order. Studia Mathematica, Tome 129 (1998) pp. 263-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i3p263bwm/

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