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title
Ngô Quốc Anh
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In math we trust, the rest we suspect
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Ngô Quốc Anh
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2026-02-18 17:02:44
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Ngô Quốc Anh | In math we trust, the rest we suspect Ngô Quốc Anh February 25, 2023 A weak form of several ODEs via integration by parts Filed under: Uncategorized — Ngô Quốc Anh @ 21:59 In this note, we shall discuss the weak form of several ODEs via integration by parts. To be more precise, we are interested in the following two simple ODEs in and in where the given function is assumed to be continuous. 1. THE CASE OF Initially, if solves in the classical sense, then must be of class . We call a strong solution. In the weak sense, we can only assume that is continuous. But we need more conditions. To be exact, we require the following holds for any test function with . If the above is satisfied, we call a weak solution. We shall prove the following Theorem 1. Assume that . Then any weak solution to is also a strong solution. (more…) Leave a Comment June 3, 2022 Non-zero derivative does not imply the continuity of the in...
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