Resumo

LOZA ROJAS, César. Quasilinear Theory of Kato. Rev. Mat [online]. 2018, vol.25, n.2, pp.319-345. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v25i2.33617.

[16]

In the present paper we will analyze the local Cauchy problem associated with the Korteweg-De Vries (KdV) equation in H s with s > 3/2. The objective of this work is to establish the good local formulation of the problem when u 0 ∈ H s , s > 3/2, for this we apply the quasi-linear theory of Kato, which consists of (06) hypotheses, in the linear case and (08) hypotheses in the non-linear case. In the solution of Cauchy’s problem for the quasi-linear equation of evolution, we will rely on Banach’s fixed-point theorem.

Palavras-chave : teorema de existencia local y unicidad; existencia de soluciones generalizadas; aplicaciones de EDP en áreas distintas de la física.

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