Mathematics Subject Classification: 35A07, 35D05, 35Q80.
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Artículos
Teoría Cuasilineal de Kato
Quasilinear Theory of Kato
1Departmento de Matemática, Universidad Nacional San Luis Gonzaga, Ica, Perú. E-Mail: lozacr@gmail.com
En el presente artículo analizaremos el problema de Cauchy local asociado a la ecuación de Korteweg-De Vries (KdV) en H s con s > 3/2. El objetivo de este trabajo, consiste en establecer la buena formulación local del problema cuando u 0 ∈ H s , s > 3/2, para ello aplicaremos la teoría cuasi-lineal de Kato, el cual consta de (06) hipótesis, en el caso lineal y (08) hipótesis en el caso no-lineal. En la solución del problema de Cauchy para la ecuación de evolución cuasi-lineal, nos basaremos en el teorema del punto fijo de Banach.
Palabras clave: teorema de existencia local y unicidad; existencia de soluciones generalizadas; aplicaciones de EDP en áreas distintas de la física
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.
[17]Mathematics Subject Classification: 35A07, 35D05, 35Q80.
[22]Ver contenido en pdf.
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Received: June 14, 2017; Revised: April 28, 2018; Accepted: April 27, 2018