Div-curl lemma revisited: Applications in electromagnetism
نویسندگان
چکیده
Two new time-dependent versions of div-curl results in a bounded domain Ω ⊂ R are presented. We study a limit of the product vkwk, where the sequences vk and wk belong to L2(Ω). In Theorem 2.1 we assume that ∇× vk is bounded in the Lp-norm and ∇ ·wk is controlled in the Lr-norm. In Theorem 2.2 we suppose that ∇ ×wk is bounded in the Lp-norm and ∇ · wk is controlled in the Lr-norm. The time derivative of wk is bounded in both cases in the norm of H(Ω). The convergence (in the sense of distributions) of vkwk to the product vw of weak limits of vk and wk is shown.
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ورودعنوان ژورنال:
- Kybernetika
دوره 46 شماره
صفحات -
تاریخ انتشار 2010