Wellposedness of a Cauchy Problem Associated to n-th Order Equation

• DOI: https://doi.org/10.22533/at.ed.5032528014

• Palavras-chave: '

• Keywords: 'Groups theory, n-th order equation, existence of solution, conservative property, Periodic Sobolev spaces, Fourier Theory.

• Abstract:

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  In this article we prove that the Cauchy problem associated to n-th order equation in periodic Sobolev spaces is globally well posed when n is an odd number such that n − 1 is an even number not multiple of four. We do this in an intuitive way using Fourier theory and in a fine version using groups theory. Also, we demonstrate the conservative property of the Cauchy problem using differential calculus in Hpers  .

  Finally, we study its generalization for the other cases of n.