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Titlebook: Evolution Equations of von Karman Type; Pascal Cherrier,Albert Milani Book 2015 Springer International Publishing Switzerland 2015 35K55,3

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楼主: ODE
发表于 2025-3-25 04:06:16 | 显示全部楼层
Weak Solutions,f our knowledge, uniqueness of weak solutions to problem (VKH) is open, and presumably not to be expected; in contrast, uniqueness does hold in the physically relevant case of the von Karman equations (3) and (4) in ., that is, when . = 1; we briefly comment of this result, due to Favini et al., [16
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The Parabolic Case,, for some . ∈ ]0, .] independent of .. This means that, under the assumption (.) (that is, again, .. ∈ .. and .), we show that there is . ∈ ]0, .], independent of ., and a unique ., solution of problem (VKP). In addition, this solution depends continuously on the data .. and ., in the sense of (.).
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Weak Solutions,quired when . = 2 is actually necessary. On the other hand, we point out that weak solutions of problem (VKH) are global in time; that is, they are defined on the whole time interval [0, .] on which the source term . is given.
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