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Non-uniform dependence on initial data for the \({\mu-b}\) equation. (English) Zbl 1277.35039

Summary: This paper is concerned with the non-uniform dependence on initial data for the \(\mu\)-\(b\) equation on the circle. Using the approximate solution method, we construct two solution sequences to show that the data-to-solution map of the Cauchy problem of the \(\mu\)-\(b\) equation is not uniformly continuous in \({H^s(\mathbb{S})}\).

MSC:

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
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