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Uniqueness class of the wave equation on graphs

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 Added by Fengwen Han
 Publication date 2020
  fields
and research's language is English




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We study the wave equation on infinite graphs. On one hand, in contrast to the wave equation on manifolds, we construct an example for the non-uniqueness for the Cauchy problem of the wave equation on graphs. On the other hand, we obtain a sharp uniqueness class for the solutions of the wave equation. The result follows from the time analyticity of the solutions to the wave equation in the uniqueness class.



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