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...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | Colombia |
| Institución: | Universidad Nacional de Colombia |
| Repositorio: | Repositorio UN |
| Idioma: | español |
| OAI Identifier: | oai:repositorio.unal.edu.co:unal/80230 |
| Acceso en línea: | https://repositorio.unal.edu.co/handle/unal/80230 https://repositorio.unal.edu.co/ |
| Access Level: | acceso abierto |
| 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 |
| Sumario: | 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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