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Ill-posedness for the Burgers equation in Sobolev spaces

By: Contributor(s): Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 189-197pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: In this paper, we consider the Cauchy problem for the Burgers equation in the line. We shall prove that this problem is ill-posed in the Sobolev space with in the sense of “norm inflation” by constructing an explicit example of initial data.
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In this paper, we consider the Cauchy problem for the Burgers equation in the line. We shall prove that this problem is ill-posed in the Sobolev space with in the sense of “norm inflation” by constructing an explicit example of initial data.

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