On the wellposedness of the KdV-K-S equation in periodic Sobolev spaces

• DOI: 10.22533/at.ed.5432206125

• Palavras-chave: -

• Keywords: semigroups theory, existence of solution, KdV - Ku- ramoto - Sivashinski equation, nonhomogeneous equation, periodic Sobolev spaces, Fourier theory.

• Abstract:

  . In this work we prove that the Cauchy problem associated to the KdV-Kuramoto-Sivashinky (KdV-K-S) equation is globally well posed. We do this in an intuitive way using Fourier theory and in a fine version using Semigroups theory. Also, we study the corresponding nonhomogeneous problem and prove it is locally well posed and even more we obtain the continuous dependence of the solution with respect to the initial data and the non homogeneity. Finally, we prove the uniqueness solution of the homogeneous KdV- K-S equation using its dissipative property.