Local well-posedness for a Cauchy problem associated to a non linear evolution equation
DOI:
https://doi.org/10.15381/pesquimat.v24i2.21697Keywords:
non linear KdV-Kuramoto-Sivashinsky equation, periodic Sobolev spaces, local well posedness, Semigroups theory, Fourier theory, Banach's fixed point theoremAbstract
In this article we will study the local well-posedness for a non-linear Cauchy problem associated with the differential equation KdV- Kuramoto-Sivashinsky:
in the infinite dimensional spaces (periodic sobolev) H sper. We do this using the theory of C0- semigrupos, main properties of the Fourier transform in H sper, as the inmersions in these spaces and that H s-1per is a Banach algebra, which allows us to justify the presence of the non-linearity 
.
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Copyright (c) 2021 Luis Milla Garcia, Yolanda Santiago Ayala
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