Existencia de solución débil para un problema parabólico no lineal con derivadas fraccionarias
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Date
2024
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Publisher
Universidad Nacional de Trujillo
Abstract
La presente investigaci´on tiene como objetivo principal demostrar existencia de soluci´on d´ebil
para un problema parab´olico no lineal con derivadas fraccionarias para las variables espacial
y temporal sobre un dominio de dimensi´on uno. Usando el m´etodo de Variedad de Nehari y
su relaci´on con la Funci´on de fibrado se demostr´o la existencia de soluci´on d´ebil para el caso
estacionario. Finalmente usando el Teorema Azela-Ascoli y Teorema de punto fijo de Banach
se demostr´o existencia y unicidad de soluci´on d´ebil para el problema parab´olico no lineal.
The main objective of the present investigation is to demonstrate the existence of a weak solution for a nonlinear parabolic problem with fractional derivatives for the spatial and temporal variables on a one-dimensional domain. Using the Nehari Manifold method and its relationship with the Fibering Maps, the existence of a weak solution for the stationary case was demonstrated. Finally, using the Azela-Ascoli Theorem and Banach’s Fixed Point Theorem, the existence and uniqueness of a weak solution for the non-linear parabolic problem were shown.
The main objective of the present investigation is to demonstrate the existence of a weak solution for a nonlinear parabolic problem with fractional derivatives for the spatial and temporal variables on a one-dimensional domain. Using the Nehari Manifold method and its relationship with the Fibering Maps, the existence of a weak solution for the stationary case was demonstrated. Finally, using the Azela-Ascoli Theorem and Banach’s Fixed Point Theorem, the existence and uniqueness of a weak solution for the non-linear parabolic problem were shown.
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Keywords
Cálculo fraccionario, Variedad de Nehari, Operador de fibrado, Solución débil, Derivada fraccionaria