El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
In this work, we study questions related to the local well-posedness for the initial value problem associated to the partial differential equation, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, where 0 ≤ α, β ≤ 1 and p ∈ Z ^{+}, in the standard, anisotropic and weighted Sobolev spaces...
- Autores:
-
Albarracin Hernandez, Carolina
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/80230
- Palabra clave:
- 510 - Matemáticas:515 - Análisis
Cauchy problem
Function spaces
Functional analysis
Problema de Cauchy
Espacios funcionales
Análisis funcional
EDP
Espacios de Sobolev
Buen planteamiento local
PDE
Sobolev’s spaces
Local well possednes
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In this work, we study questions related to the local well-posedness for the initial value problem associated to the partial differential equation, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, where 0 ≤ α, β ≤ 1 and p ∈ Z ^{+}, in the standard, anisotropic and weighted Sobolev spaces in R × T and T^{2}. For this purpose, we use parabolic regularization, localized Strichartz and energy estimates, together with a compactness argument, as well as, commutator estimates and remarkable properties of the Stein derivative. In addition, we show the existence of certain type of solitary wave in the cylinder. |
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