Keywords
existence of generalized solutions
applications of PDE in areas other than physics
teorema de existencia local y unicidad
existencia de soluciones generalizadas
aplicaciones de EDP en áreas distintas de la física
How to Cite
Abstract
In the present paper we will analyze the local Cauchy problem associated with the Korteweg-De Vries (KdV) equation in H* with s > 3/2. The objective of this work is to establish the good local formulation of the problem when u0 ∈ H*, 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.
References
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